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AuvTool User`s Guide - WWW4 Server

1. Check Box to Name Dataset specify whether Edit Box the first row is a ei title row Edit Box to show where the current cursor is Name Dataset button View Uncertainty Batch Mode Windy Gime Sew For Help press F1 AuvTool Main Frame and Main Sheet AuvTool Main Sheet AuvTool Main Frame 22 After you start AuvTool the program will provide you with a blank sheet as shown above There are four ways to enter data You can enter data by keyboard load data from an existing AuvTool disk file import data from other file formats or use the Window copy and paste command located Edit menu in the AuvTool Main Frame to enter data 6 1 Input Data from the Keyboard You can enter data by moving the cursor highlighted cell to a cell and then typing a number Press lt Enter gt key to accept the input and the cursor will automatically move down one row Repeat this step to enter the remaining data in the column If you want to change the data in a cell just move the cursor to the cell type another value and press lt Enter gt Tip You can also use arrow key to accept the value in the current active cell and move the active cell to the next cell pointed by the arrow Note In AuvTool it is specified that each column in the Main Sheet represents one dataset If you have multiple datasets you have to enter the different datasets into different columns You
2. Bootstrap Simulation page of Bootstrap Simulation window Note I The above figure is from the Batch Bootstrap button within the Batch Fitting window There are five datasets which have original data and three datasets without original data The following figure shows the example dataset name list in the dataset combo box 64 Input Current Dataset Dataset 1 z Dataset 2 Dataset 3 Dataset 4 Dataset 5 NoData Name 1 Moment Note 2 The program by default sets the number of bootstrap simulation replications as 200 and the number of samples to simulate variability for each alternative frequency distribution as 200 However users can change these two numbers and redo the bootstrap simulation accordingly The allowable range for each of two numbers is from 200 to 2000 It is not necessary to always keep the two numbers the same Note 3 The probability bands are not available for the empirical distribution Note 4 If you want to do any editing for a graph please see the section Working with a Graph on page 100 12 1 Doing a Bootstrap Simulation Bootstrap simulation is done separately for each dataset in the dataset list box Before you can do a bootstrap simulation you must select a dataset To do this e Pull down the dataset combo list box as shown on the previous page and click on the desired dataset name e The program will update the information in the current distribution ty
3. Exporting Fitting Result Summary Table You can export the fitting results to other file formats or to your applications You can copy save and export the fitting results summary sheet Please see the section on Working with Sheet on page 96 for more details 14 3 Exiting the Module You have two ways to exit the Variability Analysis Fitting Distribution Summary window 82 Click the OK button on the Variability Analysis Fitting Distribution Summary window Click the Cancel button on the Variability Analysis Fitting Distribution Summary window 83 15 0 UNCERTAINTY ANALYSIS RESULT REPORTING AuvTool reports three types of uncertainty analysis results They are 1 summary of the uncertainty in the mean and standard deviation 2 summary of the parametric distributions fitted to the sampling distribution data for the statistics of interest and 3 summary of results in a format specially used for EPA s SHEDS model 15 1 Reporting Uncertainty in the Mean and Standard Deviation You can get a report regarding uncertainty in the mean and standard deviation by clicking on the Uncertainty Result Summary button on the left bottom of the Batch Fitting window The program will display an Uncertainty Analysis Summary window such as the example below Uncertainty Analysis Summary x aeee eoo er E eaa E aan E Type Method 2 5 Percentile Mean 97 5 Percentile 2 1 Dataset 1 Weibull Moment 0 688012
4. NINNA n a220119 N A122271 N aonnoa neno NRATANA nannaco nanan nanarcon Cancel Apply Help These data include the 2 5 5 0 25 50 75 95 97 5 percentiles that represent probability bands these probability bands can be used to construct confidence intervals of the CDF of the distribution fitted to the data For example the 95 percent confidence interval for the CDF is enclosed by the 2 5 and 97 5 percentile bands 69 The sampling distribution data for the mean standard deviation and the distribution parameters for the current dataset being analyzed are also given Note1 The sheet only displays the bootstrap simulation data for the dataset that the user is analyzing If you want to display data for another dataset go back to the Bootstrap Simulation Graph page select the desired dataset do the bootstrap simulation and then come back to the Bootstrap Simulation Data page Note 2 For the First Parameter and Second Parameter definitions inside the above the datasheet please see Distribution Definitions and AuvTool Conventions on page 18 Note 3 To save the current data sheet or to do any operations on the datasheet please see Working with a Sheet on page 96 12 5 Entering the Module of Analyzing the Sampling Data of Statistics of Interest After you have done a bootstrap simulation you can obtain the sampling distribution data for the mean standard de
5. C Up Horizontal C Down Cancel Apply Now Help Graph Control dialog box 101 m Input ERES Fitting a Distribution for Dataset 1 Dataset 1 x Distribution Type Normal z Estimation Method Method Of Moment Sprake Copy Max Likelihood Method m Statistical Tests m K S Test ja 41475914911794 Critical Value at 0 05 Significant Level g 258 Passed or Not Passed m Anderson Darling Test Value a 158062250395989 Critical Value at 0 05 Significant Level p 752 Passed or Not Passed Working with Graph popup menu such as copying printing and saving a graph when you click the right mouse button you need to follow the steps listed below e Click the Design tab within the Graph Control dialog box The program will go to the Design page shown below Graph Control x Titles Axis Fonts m Draw Mode gt r Draw Style5 r New Line r Hot Graphing Draw Mono Character J On Cursor C Blit Color afal Whenever the Graph Control dialog box is invoked this check box will be checked Run Time on Right Click T Run Time HelpFile GRAPHPPR HLP Browse JS Wesia7 Time m Clip Graph Caption Graph Control I Clip To Axes Run Time Options Disable Page and Icon C Disable Page Enable Event M Galey M Stile M Data TT Titles J Ax
6. above window The figure on the next page displays the distribution information for all variables included in the example used in the User s Guide The example was introduced on page 23 Note 1 The figure shown on the next page comes from the Batch Fitting window Therefore in the example the check box labeled Included variables without data is enabled Ifthe Variability Analysis Fitting Distribution Summary window is opened from the Fit a Single Distribution window then the check box will be disabled Note 2 For those variables without original data there are no K S test or A D test results available The cells associated with the tests will be marked as NA 80 Variability Analysis Fitting Result Summary Ioj x Reser haine No Of Data Distribution Estimation First Second Points Type Method Parameter Parameter 1 Dataset O o Weibull Moment 0 91730 3 73194 2_ Dataset 2 Lognormal Moment 0 07159 0 54696 Dataset 3 Lognormal Moment 0 11336 0 50263 Dataset 4 Lognormal Moment 0 12989 0 47275 5 Dataset5 Normal Moment 0 65092 0 33035 Cancel Variability Analysis Fitting Distribution Summary window 3 14 1 Brief Explanation of Columns in the Fitting Result Summary Table The following briefly introduces what each column in the summary table means Dataset Name In this column the variable names are listed for the variables you analyzed No of Data Points The number of
7. second column of the sheet labeled B as shown on the next page Note If you find that there are not sufficient significant figures in reporting results for small numbers check the Scientific Notation labeled checkbox by clicking on it The program will report the results in scientific format 32 E Em 3 6000000 2 5000000 3 6000000 3 8000000 2 5000000 4 5000000 2 5000000 9 0000000 3 8000000 10 0000000 39 0000000 11 5000000 3 8000000 12 0000000 4 5000000 14 0000000 10 0000000 12 33 8 0 RANDOM SEED SETTING In this section we explain how to set a random seed for random sampling By default AuvTool has its own random seed However AuvTool provides a feature by which users can change the random seed for their special requirements You can enter the Random Seed Setting module by Pulling down the Uncertainty pull down menu and selecting Random Seed Setting The program will display the following Random Seed Setting dialog box Random Seed Setting x MV Using Default Random Seed Random Seed Setting 8 1 Using the Default Random Seed By default the program will use its own random seed If users would like to use the default random seed they do not need to invoke the module at all In some situations if users have modified the default random seed in previous analysis and they want to restore it they need to
8. 39 Fit a single distribution Input Data Sets Dataset 3 RE Dataset 1 Dataset 2 Dataset 3 Dataset 5 Method Of Moment Max Likelihood Method Go m Output Mean 0 827661 Standard Deviation e5 26 Cumulative Probability Fitting a Distribution for Dataset 1 a Data n 10 Z Normal Statistical Tests m K S Test for 41475914911794 Critical Value at 0 05 Significant Level p Passed or Not Fassed m nderson Darling Test Value a 158062250395989 Critical Value at 0 05 Significant Level p 752 Passed or Not Passed Fit a single distribution m Input Data Sets Dataset 3 hd Distribution Type Fitting Result Summary Bootstrap Fit a Single Distribution m Output Mean of Ln x for 1336 Std Dev of Ln x 0 502628 Cumulative Probability Fitting a Distribution for Dataset 3 4 Data n 50 Z Lognormal m Statistical Tests m K S Test p 0905177303572124 Critical Value at 0 05 Significant Level g 25299321626256 Passed or Not Passed Anderson Darling Test Value a 312301388331171 Critical Value at 0 05 Significant Level p 752 Passed or Not Passed Fit a Single Distribution To select a dataset e Pull down the Data Sets labeled combo list box menu on the lef
9. In the dialog box select AuvTool and press the End task button Problem In some situations there maybe have some errors in importing Excel files to the AuvTool and the import may not successful There are three reasons which might lead to the appearance of such errors 1 the Excel file format is not a Microsoft Excel 97 format 2 The Excel file you are importing into AuvTool is being used or is open in your Excel program and or 3 the Excel file is too large or has some special characters that the AuvTool cannot support 118 Solutions 1 Save the Excel file in the form of Excel 97 file format 2 Close the Excel file in your Excel program and or 3 Use the Window Copy and Paste commands introduced in the section of Data Entry Importing and Exporting on page 22 to import the data from the Excel file Problem In few cases if the sheets in the AuvTool contain a lot of data when you try to export the sheets to an Excel file the exporting may not be successful The reasons are not known Solutions 1 Export the sheet to a tab delimited text file which can later be open in the Excel application 2 Use the Window Copy and Paste commands introduced in the section on Data Entry Importing and Exporting on page 22 to export data to an Excel file Other bugs may exist At this time the software us provided at is and no support is available We would
10. Prepared by North Carolina State University for the U S Environmental Protection Agency Research Triangle Park NC February 2002 The technical report and user s guide are also available in the AuvTool software package 1 2 Purpose The purpose of this project is to develop evaluate and refine a user friendly module for the EPA Stochastic Human Exposure Dose Simulation SHEDS model The module incorporates appropriate algorithms for assigning or fitting statistical distributions to model inputs for quantifying variability in the data and features the use of bootstrap simulation for quantifying uncertainty in statistics for the data or fitted distributions However as a stand alone tool AuvTool is also generally applicable to quantifying variability and uncertainty in risk assessment emissions estimation and other quantitative analysis fields 1 3 System Requirements The AuvTool software requires the following configurations e The Intel based computer running Windows 98 Me e Any SVGA or better display at least a resolution of 800x600 or more pixels a resolution of 1024x768 is recommended e Atleast 100 Megabytes of free hard disk space e Atleast 64 Megabytes of total memory 1 4 Software Tools Used in Development of AuvTool The underlying algorithms simulation models and Graphical User Interface GUI were written in Microsoft Visual C 6 0 a standard software development tool for the Windows environment The GUI el
11. and Analyzing the Sampling Data for the Statistics of Interest module 55 10 9 Exiting the Batch Analysis Module You have two ways to exit the module e The OK button on the Batch Fitting window e Click the Close icon of the right top corner of the Batch Fitting window 56 11 0 ENTER OR LOAD DISTRIBUTIONS INFORMATION WITHOUT ORIGINAL DATA For some quantities a user may know the type of parametric distribution that others selected as a best fit to a dataset but may not have access to the data set itself As long as sufficient information about the fitted distribution is available it is still possible to estimate uncertainty in selected statistics and regarding the CDF of the parametric distribution The minimum data requirements include the type of distribution 1 e normal lognormal beta gamma Weibull uniform and symmetric triangle distribution the numerical value of the two distribution parameters and the number of data points that were used in the dataset from which the parameters were estimated The Link Distributions module introduced in this section provides a way for a user to enter information about a distribution even though the original data are not available In ture this enables users to do uncertainty analysis even though the original data are not available In this section you will learn how to provide the distribution information to the AuvTool for uncertainty analysis use You can enter the L
12. unknown distribution For example the 95 percent probability band may be thought of as a 95 confidence interval This interval has a 95 percent 66 probability of enclosing the true but unknown distribution The probability bands tend to be wider in range with very small datasets and or in situations with large variation within the available sample of data From the probability bands you can obtain a confidence interval for any percentile of the distribution 2 Uncertainty of Statistics If you click on the Uncertainty of Statistics radio button on the right hand side of the Bootstrap Simulation Graph page you will obtain a graphical display of a probability distribution for a selected statistic of the current variable A statistic is a function of a random dataset For example a mean standard deviation or distribution parameter is calculated from the random sample of data Any value calculated from a random data set is itself random A probability distribution for a statistic is referred to as a sampling distribution Sampling distributions are the basis for constructing confidence intervals The AuvTool program displays for you the sampling distribution of the statistic you select from the Uncertainty of Statistics pull down menu on the lower right of the Bootstrap Simulation Graph page The 95 percent confidence interval for that statistic is also shown and it is based on the range from the 2 5 percentile to the
13. 0 826736 0 977089 Lognormal Moment 0 835350 1 078356 1 385800 Lognormal Moment 0 883052 1 009503 1 147866 Lognormal Moment 0 951584 0 982140 1 013923 Normal Moment 0 415494 0 651159 0 868226 Normal Moment 7 497081 9 962685 12 793174 Lognormal Moment 1 519883 1 703602 1 893432 Gamma Moment 187 924497 205 114160 221 796368 as e Fim Uncertainty Analysis Summary window 1 It may take a while to get the reports which depends on the speed of your computer the number of datasets you are analyzing the bootstrap simulation parameter values and which parameter estimation method is used 84 Uncertainty Analysis Summary xi RESA Mean Std Deviation Std Deviation Method 2 5 Percentile Mean 97 5 Percentile 2 5 Percentile Mean 97 5 Percentile Moment 0 688012 0 826736 0 977089 0 129039 0 237607 0 347369 0 835350 1 078356 1 385800 0 337081 0 606995 1 05112 0 883052 1 009503 1 147866 0 376882 0 522093 0 733852 0 951584 0 982140 1 013923 0 448970 0 490640 0 536754 0 415494 0 651159 0 868226 0 172858 0 320810 0 469982 7 497081 9 962685 12 793174 3 015366 4 914352 6 864976 1 519883 1 703602 1 893432 0 280687 0 424432 0 628553 187 924497 205 114160 221 796368 31 040363 44 766731 59 796766 Uncertainty Analysis Summary window 2 15 1 1 Brief Explanation of Columns The following gives a brief introduction to the columns inside the Uncertainty Analysis Summary window Dataset Name The variable or data set name is g
14. 70768 0 87103 0 79836 0 76866 0 29154 0 20011 0 10503 0 24697 0 21314 0 27537 0 23489 0 20413 General Format Sheet 3 Std Deviation First Para 0 90528 0 86729 0 91792 0 84032 0 76648 0 9641 0 88617 0 84794 IV Display Statistical Test Results V Display Empirical Distributions of Statistics Second Para 3 23823 4 31236 9 50872 3 69489 3 55087 3 96416 3 77042 3 73078 Mean Std Deviation First Para Second Para Summary on uncertainties in mean std deviation and other statistics C EPA SHEDS Model Format General Format Second Para 3 23823 4 31236 9 50872 3 69489 3 55087 3 96416 3 77042 3 73078 General Format Sheet 4 Mean Std_Deviation First Para Second Para 92 IV Display Statistical Test Results IV Display Empirical Distributions of Statistics 0 37591 0 24793 0 21695 Std _Deviatio First Para 1 0000 0 1408 0 9854 0 4667 0 1409 1 0000 0 0232 0 8592 0 9854 0 0232 1 0000 0 3142 0 4667 0 8592 0 3142 The pair wise sampling data and correlation matrix the corresponding distributions fitted to the sampling distribution data for the statistics of the mean standard deviation distribution parameters The second part will be shown if the Display the Statistical Test Results labeled check box is selected The third part will display pair wise sampling data for all four statistics of interest and
15. 8 4 2 1 6 2 0 J Cancel Apply Help Note You can change the type of statistics whose uncertainty is displayed by pulling down the combo list box labeled Statistics and by clicking on one of the statistics The following figure displays the combo list box Uncertainty of Statistics Statistics Mean Mean Standard Deviation First Parameter SecondPara From 0 67888197371141 68 2 Ifthe program is showing a graph of uncertainty for a statistic click the Probability Band radio button to switch to a display of the probability bands for the fitted distribution for variability 12 4 Displaying and Saving the Bootstrap Simulation Data AuvTool provides the bootstrap simulation data To display or save the data click the Bootstrap Simulation Data tab page The program will display the following window Bootstrap Simulation Graph Bootstrap Simulation Data Fitting Uncertainty Sampling Distributions The current dataset Datas 25 5 0 25 50 75 95 97 5 Mean Standard First Percentile Percentile Percentile Percentile Percentile Percentile Percentile Deviation Parameter P 0 034938 0 096004 160038 0 231053 0 366725 0 408057 704284 0 229956 0 792276 0 071223 0 137527 205579 0 280050 0 405443 0 451596 899798 0 247614 1 010924 0 085962 0 167706 228513 0 305748 0 430458 0 485965 678882 0 224000 0 758898 0 096527 0 1848
16. 97 5 percentile of the sampling distribution 12 3 Switching Between Graphs of Uncertainty and Probability Bands To switch between graphs of probability bands and of uncertainty in statistics select the appropriate radio button on the right side of the Bootstrap Simulation Graph page the under the Graph of text 67 1 Ifthe AuvTool program is displaying the probability band of a variable click the Uncertainty of Statistics radio button The program will switch to show the graph of uncertainty for a selected statistic By default the graph will display the uncertainty in the mean as the following figure named the Uncertainty window Bootstrap Simulation x Bootstrap Simulation Graph Bootstrap Simulation Data l Fitting Uncertainty Sampling Distributions l Input No For Variability 500 Go Bootstrap Simulation Uncertainty Graph Uncertainty in the Mean for Dataset 1 Data Current Dataset y 3 Rani Dataset 1 x 1 0 ie pi os E 95 Percent Current Distribution Type EE 90 Percent Weibull oe E 50 Percent Current Estimation Method F Graph of Moment 3 C Probability Band 0 6 Uncertainty of Statistics Bootstrap Parameters S m Uncertainty of Statistics No Of Replication B a Statistics 500 g Mean z oO 0 2 r 95 Confidence Interval Sample Size From 06754794781 5647 fi 0 0 0 t To 0 38019181561751 0 0 0 4 0
17. See Installation below for instructions e Two pieces of documentation User s Guide and Technical Report These are included as Adobe PDF documents on the installation disk and can be opened or copied to another disk 2 2 Installation To install the AuvTool program you must use the installation program SETUP EXE provided on the installation CD ROM Simply copying the contents of the CD ROM to your hard drive will not work because the programs are on the CD ROM in compressed form Program files must be decompressed and installed in the appropriate directories to run properly Copying the contents of the distribution CD ROM to a local hard drive can speed up the installation process To run the Setup Program 1 Place the A CD ROM in your CD ROM drive 2 Click the Start button 3 Choose Run from the Start menu and 4 Type X XXXV SETUP EXE where X is the drive and directory to which you copied the installation files The Installation Program will begin Follow the instructions on the screen You also can install AuvTool as follows 2 3 1 Place the AuvTool CD ROM in the CD ROM drive 2 Double click the My Computer icon on the desktop 3 Double click the CD ROM drive in the My Computer window and 4 Double click the SETUP EXE on the CD ROM The Installation Program will begin Follow the instructions on the screen Removing AuvTool To remove the AuvTool software completely use
18. Specify the number of minor tick marks to be drawn between pairs of major ticks Through Axes labeled radio box Select this option if you want tick marks centered on the axis line Note Your selection will apply to all axes for which tick marks have been enabled Inside Axes labeled radio box Select this option if you want tick marks to be drawn only on the graph side of the axes Note Your selection will apply to all axes for which tick marks have been enabled Outside Axes labeled radio box Select this option if you want tick marks drawn outside the axes Note Your selection will apply to all axes for which tick marks have been enabled Grids Group Show labeled check box Select this option to draw grid lines perpendicular to the axis intersecting each tick mark Clear the 107 box for no grid lines Style labeled combo list box default is solid In this list box you can choose a style for grid lines The same style is applied to both X and Y grids Color labeled combo list box In this list box you can choose a color for grids from the current palette The same color is applied to both X and Y grids The default color is automatic black or white whichever provides more contrast Editing the Axes of a Graph You can edit the display of axes to your preference For example if you enter the following Maximum of X axis 2 0 Minimum of X axis 0 0 Check the Show labeled check box in the Grids group for both X axi
19. data points are given for each dataset Distribution Type The distribution type used to represent the corresponding dataset is indicated Estimation Method The estimation method used to estimate the parameters for the fitted distribution is given Typically there are two available estimation methods MLE and MoMM which are marked as MLE and Moment in the corresponding cells For those variables without original data there is no information available in some cases regarding which 81 14 2 method was used to estimate the parameters and the corresponding cell will be marked as NA First Parameter and Second Parameter The fitted distributions parameters are given for each variable Please see the Distribution Definitions and AuvTool Conventions on page 18 for more details KS test The K S test statistic value is reported for the fitted distribution Anderson Darling test The Anderson Darling test statistic value is reported for the fitted distribution Since this test is not available for the beta uniform and symmetric triangle distribution the values are reported as 0 0 or 1 0 in such cases KS Test Passed or not The corresponding cell will be marked as Passed or Failed If no information is available NA will be reported AD Test Passed or not The corresponding cell will be marked as Passed or Failed If no information is available NA will be reported
20. exit the module e The OK button or Cancel button on the Fit a Single Distribution window e Click the Close icon of the right corner of the Fit a Single Distribution window 43 10 0 CHARACTERIZATION OF VARIABILITY AND UNCERTAINTY BATCH ANALYSIS This section describes the Characterization of Variability Batch Analysis module in AuvTool used to quantify variability for multiple datasets This module helps users automatically analyze multiple datasets However it also allows users to select a parameter estimation method and a fit to a dataset based on their own judgment Therefore it provides a flexible way for users to do variability analysis Auto is not a distribution type It is an option The arithmetic standard deviation of each dataset The arithmetic mean of each dataset Batch Fitting Eoix Distribution Choice Variable Name Dae Lognormal Gamma w p 5 foo ro J Automatic Batch Analsyis for Uncertainty Sampling Distributions Save Fitting Result Summary Batch Bootstrap Uncertainty Sampling Summary Load Uncertainty Result Summary OK Batch Fitting 1 Method of Matching Mon y C Mar Likelihood Estima This Setting group is used to automatically batch analyze the sampling distribution for the statistics of interest Batch analysis data and property sheet You ca
21. explained below Variable Name The variable names for the variables you analyzed Variability Distribution The distribution type used to represent variability for the variable 88 Summary on uncertainties in mean std deviation and other statistics EPA SHEDS Model Format J Display Statistical Test Results C General Format J Display Empirical Distributions of Statistics A Variabilit 1st Parameter Uncetainty Dist _ vaiionane sia nan Vesritees weibull 2 Dataset 2 Lognormal Lognormal Lognormal Normal Normal EPA SHEDS Model Format Sheet 1 Summary on uncertainties in mean std deviation and other statistics EPA SHEDS Model Format ja Display Statistical Test Results C General Format I Display Empirical Distributions of Statistics 4th Para 2nd Parameter Uncetainty Dist For ia Variable Name M ond Para 1 30224 0 35335 Dataset 2 0 66642 0 18889 Dataset 3 0 71438 0 13827 Dataset 4 0 75279 0 03121 5 Dataset 5 9 69309 20 97861 6 NoData Name 1 1 56480 0 20155 NoData Name 2 0 24349 0 03954 8 NoData Name 3 10 39624 0 93272 Cancel EPA SHEDS Model Forma Sheet 2 89 1 Parameter V The estimated first parameter in the case of a parametric distribution for the distribution representing variability Uncertainty Dist For 1 Para The parametric distribution type describing the sampling distribution data for the estimated
22. following e Pull down the Edit menu and select the Copy e Click the Copy button on the toolbar on the left side of the AuvTool e Press Ctrl C Paste To paste data from a spreadsheet 1 Select the cells that you want to paste data into 2 Do any one of the following e Pull down the Edit menu and select the Paste e Click the Paste button on the toolbar on the left side of the AuvTool e Press Ctrl V 6 5 Exporting Data from AuvTool Main Sheet AuvTool provides features to save the current main data sheet or to export the current datasheet to other file formats such as Microsoft Excel or tab delimited text AuvTool also can make use of Window Copy and Paste features introduced above to export data to other application programs To save the current data sheet e Pull down the File pull down menu or press Alt F and select Save or Save as or just click the Save icon on the tool bar The program will display an Save as file dialog box e Enter a filename with an extension of ss3 Click the Save button in the Save as dialog box To export the current data sheet to a Microsoft Excel file format 26 e Pull down the File pull down menu or press Alt F and select Export Excel The program will display an Save as file dialog box with the initial file type of xls e Enter a filename with an extension of xls Click the Save button in the Save as dialog box Note In order to make sure that your dat
23. for each variable and the correlation between the statistics for each variable As an example the columns covering the mean statistic are explained below The columns covering the other statistics have the same explanations Variable Name The variable names for the variables you analyzed No of Data Points The number of sampling distribution data for the statistics The number is the same number as bootstrap replications Distribution The parametric distribution type used to represent the sampling distribution of the mean Method The estimation method used to estimate the parameters for the distribution fitted to the sampling distribution data These include two estimation methods MLE and MoMM which are marked as MLE and Moment respectively at the corresponding cells First Para and Second Para The parameters for the distribution fitted to the sampling distribution data for a statistic Please see the Distribution Definitions and AuvTool Conventions on page 18 for more details KS Value The K S test statistic value for the distribution fitted to the sampling distribution data for the mean AD Value The Anderson Darling test statistic value for the distribution to to the sampling distribution data for the mean Since the test is not available for 93 beta uniform and symmetric triangle distributions the values will be reported as 0 0 or 1 0 in these cases KS Passed If the K S test was pass
24. how to do uncertainty analysis using bootstrap simulation You can enter the Uncertainty Analysis Bootstrap Simulation module by clicking on the Bootstrap button on the Fit a Single Distribution window or by clicking on the Batch Bootstrap button on the left bottom comer of the Batch Fitting window or by clicking the Bootstrap button inside the batch analysis data and property sheet on Batch Fitting window More details on how to enter the module can be found in the discussion for Enter the Uncertainty Analysis Module in the section of Characterization of Variability Fitting Distribution Dataset by Dataset on page 36 and in the section of Characterization of Variability and Uncertainty Batch Analysis on page 44 Regardless of how you enter the Uncertainty Analysis Bootstrap Simulation module the program will pop up a Bootstrap Simulation window as shown on the next page There are three tab pages shown at the top within the Bootstrap Simulation window which are the Bootstrap Simulation Graph page the Bootstrap Simulation Data page and the Fitting Uncertainty Sampling page The program will by default show the probability bands of the first dataset or variable of the dataset listed on the Bootstrap Simulation Graph page The probability bands depict a 50 percent a 90 percent and a 95 percent confidence interval of the CDF of the distribution fitted to the data The user can display o
25. include the origin zero and to extend far enough in the positive and negative directions so as to include all of the graph s values Variable Origin labeled radio box Select this option to have the axes zoom in on the range of the graph s actual values whether or not that range includes origin User Defined labeled radio box in the Scale group Select this option to set your own values for the minimum maximum and number of ticks for the axis When you select User Defined the settings in the Range group are enabled Range Group Max Min and Ticks edit boxes The settings are enabled only when you select the User Defined labeled radio box in the Scale group These edit boxes are used to set the maximum point minimum point and the number of ticks for the selected axis Tick Marks Group Show labeled check box Check this box to draw tick marks along the axis Clear the box for no tick marks Every labeled edit box in the Tick Marks group If you select Zero Origin or Variable Origin in the Scale group you can use the 106 Every setting to specify the frequency with which tick marks are displayed along the X axis An Every setting of places a mark at each tick a setting of 2 places a mark at every other tick and so on The X axis must end with a tick mark If you set an Every value that does not include the last value on the axis the Graph Control will extend the axis so that it ends on a tick mark Minor labeled edit box
26. with tab delimiters between numbers You should specify a file to import by clicking on it or inputting the file name File Save Ctrl S This command saves the data in the active data sheet to disk File Save As This command lets you save the active data sheet to a different name in a different directory or on a different drive When you choose this command the Save File As dialog box is displayed This Save File As dialog box is similar to the Open Sheet dialog box You can enter the new name optionally with drive and directory and click the Save button to accept the dialog box input 12 File Print Preview This command lets you see an on screen preview of how the data sheet will appear on a printed paper File Print This command lets you print the active sheet data Please make sure that a printer is properly connected to your computer and that it is turned on before you choose this command File Printer Setup This command lets you select a target printer for data sheet output This command displays the standard Windows Print Setup dialog box that you can use to set up your printer File Exit This command exits AuvTool removes it from memory and returns you to the Windows environment If you have made any changes that you have not saved AuvTool asks you if you want to save them before exiting 4 2 Edit Menu The menu commands listed in the Edit Menu will apply to the AuvTool Main Sheet Edit Cut
27. 133 Exiting th Modul ineniosansenreue a E R E TE VARIABILITY ANALYSIS RESULT REPORTING ssessseessecesoossoesssesssese 79 14 1 Brief Explanation of Columns in the Fitting Result Summary Table 81 14 2 Exporting Fitting Result Summary Table oo ee eceeeeeeceneeneeeeeeeeenaee 82 14 3 Exiting the Modul ics cioy al ctaccenivdis eas eben cae 82 UNCERTAINTY ANALYSIS RESULT REPORTING essseesssesssesssesssesssoees 84 15 1 Reporting Uncertainty in the Mean and Standard Deviation 84 15 2 Reporting the Summary of the Fitted Parametric Distributions to Sampling Distribution Data for Statistics of Interest eee eeeeeeeeeee 87 WORKING WITH A SHEET ssscsssssccsscsssnessssssiscsdscoceutepessscnciosvendasecdschcssbersianends 96 WGN PAINS cy etree hel EET E AE E E Sted ae 96 16 2 Pasting 2icet viet errata eee Ae wate RE A Ga Mt RA aaa ae 96 16 3 Printing a SHC sis icivesdicrssivenexastecasstuceiataix kien daattea teeta lacie 97 16 4 Exporting a Sheet to Tab Delimited Text File cece eeceseesreeeeeeeeeeee 98 16 5 Exporting a Sheet to a Microsoft Excel File ceceeceseesseeseeereeeeeeeeeeaes 98 WORKING WITH A GRAPH sisciscscssecsoosssscssonsecdscocseccossusonsevsosuenssonssncssvepsesios 100 17 1 Switching between the Working with Graph Popup Menu and Graph Contr l Dialog BOX cinirenen ai mbes haves E AREA 100 17 2 Editing a Craps ne ioneroireai ae a E Meee oad ae a E s 103 17 3 Copying a Graph to Clipboard sses
28. 29 248279 0 328989 0 461568 0 500799 939681 0 199391 1 025726 0 111032 0 197000 264167 0 343204 0 478061 0 518790 868954 0 233184 0 955657 0 122677 0 210283 282690 0 358487 0 487119 0 534432 951654 0 268971 1 050606 0 128767 0 223182 298085 0 373321 0 497642 0 546086 754825 0 246844 0 840814 0 138630 0 231519 309430 0 384932 0 511008 0 549029 909269 0 220701 1 009090 0 143779 0 242623 316065 0 393938 0 525308 0 559793 906077 0 247277 0 999084 0 152535 0 250433 325500 0 401833 0 529102 0 563225 934639 0 263095 1 043014 0 159600 0 261619 335413 0 409562 0 546220 0 589558 766579 0 292287 0 660379 0 166995 0 268153 344053 0 419143 0 549117 0 595928 905737 0 300435 1 011235 0 172261 0 277745 351320 0 426145 0 560266 0 600910 843718 0 176350 0 913497 0 177864 0 283495 359599 0 436004 0 568513 0 604215 864943 0 230747 0 954605 0 182892 0 287071 368884 0 442725 0 572844 0 607105 834175 0 335634 0 968947 0 188666 0 293855 375746 0 447965 0 575187 0 611011 964597 0 188018 1 042179 0 192741 0 298169 378252 0 454727 0 578856 0 612767 861786 0 260408 0 966500 0 198722 0 302213 384481 0 461097 0 565521 0 619927 846587 0 269452 0 963425 0 203415 0 307198 391115 0 467120 0 590677 0 630218 734269 0 264996 0 819336 0 205443 0 314704 0 395680 0 473408 0 590814 0 635106 71434 0 280859 0 812667 0 211917 0 318298 0 401261 0 477621 0 600088 0 639040 0 863370 0 232206 0 946232 0 216223 0 323105 0 406695 0 483535 0 601144 0 643577 0 845724 0 228619 0 930440
29. 7 Passed or Noy Failed Statistic of s A Interests Anderson ararneier combo list box Darling test estimates information N Type of parametric The fitted Parameter distribution fitted to the distribution to Estimation sampling data of a the original Methods statistic datasets WARNING The user of AuvTool is cautioned that the availability of a batch mode technique for choosing a distribution based upon the K S test is not a substitute for the use of judgment The K S test is based upon a specific criterion which may or may not be important to a particular analyst or decision maker in the 73 context of a specific problem The K S test does not screen for results that may be physically implausible such as a probability of sampling negative values for a quantity that must be non negative The appropriateness of selection of a distribution depends on the data quality objective of each analysis which may differ from one situation to another Therefore uncritical application of the batch mode feature of AuvTool for seeking a best fit distribution is likely to lead to inappropriate selection of a probability distribution model in some cases It is the user s responsibility to evaluate the automatically selected parametric probability distribution for appropriateness with respect to the user s own criteri
30. AuvTool User s Guide Prepared by Junyu Zheng H Christopher Frey Ph D Computational Laboratory for Energy Air and Risk Department of Civil Engineering North Carolina State University Raleigh NC Prepared for Office of Research and Development U S Environmental Protection Agency Research Triangle Park NC February 2002 Acknowledgments The authors acknowledge the support of the Office of Research and Development ORD of the U S Environmental Protection Agency which funded this work via contract ID S794 NTEX Disclaimer This paper has not been subject to any EPA review Therefore it does not necessarily reflect the views of the Agency and no official endorsement should be inferred The opinions findings and conclusions expressed represent those of the authors and not necessarily the EPA Any mention of company or product names does not constitute an endorsement by the EPA 1 0 2 0 3 0 4 0 5 0 6 0 Contents EN PRODUC TIONG sass sesiinsssvescessssseucsssais sansstsilccescupeadebsctnckonelgusiusiacubestadionossaisoaters I 1 1 Whatis AV GOL ihe les curated eg a Me ccm tended anata Melee Laat 1 L2 PURPOSE eiren secup tat a a a A A AR dap baneucedsen sates RS 1 1 3 System REGUIFEMENTS sieniin aad eit a aa ia SS 2 1 4 Software Tools Used in Development of AuvTool s ssssssssnsssseseesseessesse 2 LS Using Online Help Documentation s ssseseeseeseesseesesseesseserssressessrssressesse 3 1 6 Discl
31. Coia Fitting a Distribution for Dataset 1 pee Dataset 1 Value ai 37172402058488 Current Distribution Weibul Critical Value at 0 05 Significant Level Estimation Method ose Moment Passed or Not 4 Data Passed r Output n 10 Alpha Shape Parameter g m nderson Darling Test j Value pos 7298688035972 7 Weibull E Beta Scale Parameter 6 eee Critical Value at 0 05 gg 94482864055 Significant Level e757 Passed or Not Passed 48 If the dataset you select does not have original data the dialog box will look like Fitted Distribution to the selected dataset Mie E r Status Current Dataset Current Distribution Estimation Method MLE NeData Name 2 Legnormal M Output Mean of Lnf x 0 5 Std Dev of Ln 0 25 Cumulative Probability 0 6 Fitting a Distribution for NoData Name 2 Lognormal Statistical Tests Critical Value at 0 05 Significant Level p Passed or Not 7 m AndersonVarling lest Value 0 Critica Value at O05 Significant Level Cancel Note 1 In the first case shown on the previous page the user chose Dataset 1 and the Auto option for the distribution choice and MoMM as the parameter estimation method Users cannot modify any information inside the dialog box except for editing
32. Ctrl X The Edit Cut command removes the selected data block from your data sheet and places the data in the Clipboard The removed data cells are filled with blank cells You can paste that data into any other data sheet or somewhere else by choosing the Edit 13 Paste command The data remains in the Clipboard so that you can paste the same data many times Edit Copy Ctrl C The Edit Copy command places the selected data in the Clipboardand leaves the selected data intact You can then paste that data into any other data sheet or any other editors by choosing Edit Paste command Edit Paste Ctrl P The Edit Paste command puts data from the Clipboard into the current data sheet at the cursor position This action depends on what you have in the Clipboard If the data in the Clipboard contains columns rows then it will paste data in columns starting at the column row which contains the cursor cell if the data in the Clipboard contains only a block of data cells then the paste action will put the data to the sheet starting at the current cursor cell The paste action overwrites data in the data sheet It does not insert data into the data sheet Edit Delete The Edit Delete command works like the Edit Clear command It removes the selected data from the data sheet but does not place it into the Clipboard This command also shifts the data sheet so that there are no blank cells Edit Insert This menu item has a
33. Dataset 1 Dataset 2 Dataset 3 ie FS 9 NoData Name 1500 10 NoDeta Name 2200 11 NoData Name 3200 Variable Name No Of Data General Format Sheet 1 200 500 200 1000 200 200 500 200 a aay ae ees eae ee ee a ee e ee es Variable Name No Of Data Cancel Distribution information about the statistics IV Display Statistical Test Results Distribu Normal Lognorr Lognorr Lognorr Beta Normal Lognorr Gamme KS Valu 0 0469 0 0267 Statistical test results Summary on uncertainties in mean std deviation and other statistics C EPA SHEDS Model Format f General Format Std_Deviatio Method Moment Moment Moment Moment Moment Moment Moment Moment Std_Deviatio KS Passed Passed Passed General Format Sheet 2 First Para 0 22192 0 53526 0 74741 0 71419 11 01288 4 92261 0 87282 42 29934 AD Value 0 26856 0 65413 91 IV Display Statistical Test Results IV Display Empirical Distributions of Statistics First Para Second Para 0 05266 0 29410 0 16749 0 04345 23 61432 0 96414 0 21131 1 04796 First Para AD Passed Passed Passed Cancel Summary on uncertainties in mean std deviation and other statistics C EPA SHEDS Model Format General Format NoData Name 1500 21 NoData Name 2200 22 NoData Name 3200 Mean 0 80867 0 78883 0 87149 0 75450 0
34. G ANY PARTY S INTELLECTUAL PROPERTY OR II THAT THIS REPORT IS SUITABLE TO ANY PARTICULAR USER S CIRCUMSTANCE OR B ASSUMES RESPONSIBILITY FOR ANY DAMAGES OR OTHER LIABILITY WHATSOEVER INCLUDING ANY CONSEQUENTIAL DAMAGES EVEN IF EPA OR ANY EPA REPRESENTATIVE HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES RESULTING FROM YOUR SELECTION OR USE OF THIS REPORT OR ANY INFORMATION APPARATUS METHOD PROCESS OR SIMILAR ITEM DISCLOSED IN THIS REPORT 1 7 Copyright Notices Graphics Server 5 0A Copyright 1996 Bits Per Second Ltd and Pinnacle Publishing Inc All Rights Reserved Spread 3 0 Copyright 1998 FarPoint Technologies Inc All Rights Reserved Microsoft Visual C 6 0 Copyright 1999 Microsoft Corporation All Rights Reserved Analysis of Uncertainty and Variability Tool AuvTool and Interface AuvTool 1 0 Copyright 2001 North Carolina State University All Rights Reserved Graphics Server is a trademark of Bits Per Second Ltd Microsoft is a registered trademark Windows Windows 95 and Visual C are trademarks of Microsoft Corporation Spread is a trademark of FarPoint Technologies Inc 2 0 INSTALLING AuvTool 2 1 What is Included in the Installation Package The AuvTool installation package contains the following items e Installation CD ROM All the software is on the CD ROM in compressed form An installation program included on the CD ROM will install the necessary files automatically
35. RATORS In this section we will describe how to generate random numbers by specifying a distribution type its parameters and the number of random samples you want to generate You can enter the Random Sample Generators module by pulling down the Uncertainty pull down menu and selecting Random Generator The program will display the Random Sample Generator dialog box as shown below Edit box to enter the parameters of the specified distribution Check box to use scientific notation Pull down combo box to select parametric distribution Random Sample Gen m Random Sam Input entific notation SampleDataset B al ea 0 406954 First Parameter Second Parameter 1 1943421 ERE 1 8065050 Distribution Type 1 0032052 0 2339091 0 4731102 No Of Samples 13463134 af 0 7983070 EN 0 9268961 Era 1 6646559 are 1 7144491 ra 1 5471720 Cancel The Generate Button invokes the event of generating samples The sheet to hold the generated samples The number of samples to be generated 30 In the above dialog box we have specified a normal distribution with mean of 1 0 and standard deviation of 0 5 and generated 100 random samples from the distribution The results are displayed in the spreadsheet on the right side Note 1 For First parameter and Second Parameter defi
36. Smaller Bigger T Italic F i M Bold g g 2 P Underline Reset Cancel Apply Now Help The Fonts page within the Graph Control dialog box the Fonts tab in the Graph Control dialog box to enable the Fonts page which is shown above Introduction to the Controls within the Fonts Page The Fonts page contains three groups each of which are described Apply to Group Graph Title labeled radio box Select this option to apply font settings to the graph s title which always appears centered at the top of the graphing window Other Titles labeled radio box Select this option to apply font settings to the graph s left right and bottom titles The same settings apply to all three of these titles 113 Labels labeled radio box Select this option to apply font settings to the axis labels The same settings apply to all labels in use in the graph Legend labeled radio box Select this option to apply font settings to the graph s legend Typeface Group Name labeled combo list box default is Arial In this list box you can choose any installed Windows font for the selected text Italic labeled check box default is off Select this option to have the Graph Control italicize the text Bold labeled check box default is on in the AuvTool Select this option to have the Graph Control display the text in boldface Underline labeled check box default is off Select this option to ha
37. TISTICS OF INTEREST In this section we will describe how to fit a distribution to represent the sampling distribution data of the statistics of interest that were obtained from bootstrap simulations for the datasets or variables that you are analyzing Basically this module is very similar to the Charterization of Variability Fitting Distribution Dataset by Dataset module on page 36 The main difference is that the former analyzes the sampling distribution data of statistics of interest from bootstrap simulation for a chosen dataset while the later focuses on characterizing variability for an original dataset Another difference is that this module also has a feature which can automatically help users to choose a best fit to the sampling distribution data of a statistic while the later does not Before you can enter into the module of Analyzing the Sampling Data of the Statistics of Interest first you need to enter into the module of Uncertainty Analysis Bootstrap Simulation Please refer to the Uncertainty Analysis Bootstrap Simulation module on page 63 for more details When the Uncertainty Analysis Bootstrap Simulation module is active there is a Bootstrap Simulation window with three tab pages shown as on page 73 From there you can enter into the Analyzing the Sampling Data of the Statistics of Interest module by clicking on the Fitting Uncertainty Samplin
38. a and needs Note 1 Whenever you enter into the module if there are some datasets for which bootstrap simulations have not been completed the program will provide a warning message box to tell you which datasets have not been analyzed using bootstrap simulation You will not have sampling distribution data to analyze in this module for such datasets If you want to analyze the sampling distribution data of statistics of interest for such datasets you will need to go back to the Bootstrap Simulation Graph page to do bootstrap simulation See the module of Uncertainty Analysis Bootstrap Simulation on page 63 for more details Then come back to the module to complete analysis on those datasets Note 2 Initially AuvTool assigns Auto to the Distribution Type labeled combo list box for all statistics of interest and for all datasets This means that the program will automatically help users to choose a best distribution for the statistics of 74 interests if users accept the default settings In addition the program uses MoMM as the default parameter estimation method Note 3 For some distribution types MLE or MoMM and A D tests are not available Please refer to Table 9 1 and Table 9 2 on pages 40 and 41 respectively Note 4 For some datasets particular distributions cannot be used to fit to them For example lognormal gamma and Weibull distributions cannot be used to describe datasets in which there are some negative v
39. a will not be lost we recommend that you also save your current datasheets as an AuvTool file format when you export your data to a Microsoft Excel file Please also refer to the Troubleshooting section on page 118 To export the current data sheet to a Tab Delimited Text file format e Pull down the File pull down menu or press Alt F and select Export Tab Delimited The program will display an Save as file dialog box with the initial file type of txt e Enter a filename with an extension of txt Click the Save button in the Save as dialog box Note When you save a file you can save the file to any other directory you want Just select the drive letter and the directory you want to save to in the Directories box You can also save the file to a floppy disk In order to do that just change the drive to the drive letter of your disk 6 6 Naming a Dataset AuvTool requires that user must name each dataset inside the AuvTool main sheet As introduced above each column stands for a dataset The figure shown on the next page displays how the AuvTool Name Dataset feature works 27 To name a dataset e Select the column where the dataset you want to name is located or place the cursor inside any cells of the column e Enter names into the Name Dataset labeled edit box directly above the spreadsheet Click the Name Dataset button and the name representing the dataset you just specified will be disp
40. able In this situation the MLE radio box is disabled For the empirical distribution neither MLE nor MoMM are applicable so both of the radio boxes are disabled in this case 9 4 Variability Analysis Results Summary for All Datasets After you have reviewed or modified the selection of parametric probability distributions and parameter estimation method you can obtain a summary of the distributions parameters of distributions associated with each dataset parameter estimation method used and statistical test results To do this e Click the Fitting Result Summary button on the Fit a Single Distribution window e The program will display a popup Fitting Result Summary dialog box More information can be found on Variability Analysis Result Reporting on page 79 9 5 Entering Uncertainty Analysis Module The decisions or choices of distribution types and parameter estimation methods you made in the Characterization of Variability Fitting Distributions Dataset by Dataset module will provide a basis for uncertainty analysis using bootstrap simulation To enter the uncertainty analysis module e Click the Bootstrap button on the Fit a Single Distribution window 42 e The program will display a popup Bootstrap Simulation dialog box with three tab pages More information on uncertainty analysis can be found on Uncertainty Analysis Bootstrap Simulation on page 63 9 6 Exiting the Module You have two ways to
41. aimer of Warranties and Limitation of Liabilities 0 4 17 C pyright INGUCES ix tsiecadeechasssaniactsantadiiecsace dansancsoanyagdanelzesseuracalbas iai 4 INSTAL DING AUVTOOL e cicsssscesssnenscussssctasdesensensssdenssnstvasensiatsnseveoesesensseusesteesin 6 2 1 What is Included in the Installation Package ceeccceceeseesteeeteeeteeeees 6 22s MANS TARA IN Seca och v Cactus hse a a e a e aera gsi vc ede cause Se 6 2 3 Removing Avy 1 GO sint o tues aa east aot aili 7 GETTINGSTARTED pisccusstinciiccasaieseasanciivedsnieieesuaciceassotseelansusteteatoavceaseaveasencaanns 8 3 1 Starting AUV Toolsi an o aE i 8 Be US AAI OO r a A N N A A ewe case 8 3 3 EXAINS AUV 00 le senian tition aia a nae E E A E E A sates 10 INTRODUCTION TO AUVTOOL MAINFRAME MENUS cesesssseeeee 11 4 1 File MA G10 sannri cay eats anaes evade acne a soda sca a peas e eta aga 11 42 Edit IM wins saosin ape bat endd a sco ate EE a ATAA AARE on aR aT 13 BS View Meninis m ee yee E e E ee ce a ak Soa eS a 15 44 Wncertainty Men sanera nii g aaa E ERE 16 4S Batch Mode M h ssereiien dienaa er ieia 16 4 6 Window Menun aa aac ln Sea n a So Caen Ea aaa ae 17 Al IHEM en esea E ial E E A NR 17 PROBABILITY DISTRIBUTION DEFINITIONS AND AUVTOOL CONVENTIONS siatisieivastaccidetssicutoiozaiorons sanastasstionetesmasvenensautaruamssvclantarcastnieouuany 18 5 1 Definitions of Parametric Probability Distributions 0 eee 18 5 2 Empirical Distribution icici Gan
42. ake 24 sure the data file contains only numerical values except for text strings that are contained in the first row or the column headers Otherwise the program will provide a warning message box to show you that the text in a particular cell is not a valid numerical value You must correct all the mistakes before you can do further analysis For more information see Data Input Checking on page 31 To import data to AuvTool from Microsoft Excel files or Tab Delimited files e Pull down the File pull down menu or press Alt F and select File Import Excel or File Import Tab Delimited File the program will display an Open file dialog box e Find the file name that you would like to open Click the Open button in the Open dialog box Note AuvTool can only support importing a 97 Microsoft Excel file format Make sure that your datasheet files are saved in the form of 97 Microsoft Excel file For some rare cases if you find that you cannot import an Excel data file you also can use the following Window Copy and Paste features to import your data 6 4 Windows Copy and Paste Data can also be imported or exported by using Windows Copy and Paste command which are often listed in the Edit menu between the Windows application programs based on a spreedsheet such as Excel Access and AuvTool Copy To copy data from a spreadsheet 1 Select the cells that you want to copy 25 2 Do any one of the
43. al data 50 Note 2 No graphs will be displayed when the distribution types cannot be used to describe a dataset For example in the figure of the previous page the graph of the beta distribution is not available because not all values in the dataset fall between 0 and 1 10 3 Entering Uncertainty Analysis Module In the Batch Analysis module there are two ways to enter the Uncertainty Analysis Bootstrap Simulation module One is that you can click on the Bootstrap button inside the batch analysis data and property sheet another is that you can click the on Batch Bootstrap button on the left bottom corner of the Batching Fitting dialog box The difference is that bootstrap simulation will only be done on the dataset located at the button row for the former while the later will contain all datasets inside the batch analysis data and property sheet In either case the program will bring a popup Bootstrap Simulation dialog box with three tab pages to the screen More information on uncertainty analysis can be found on Uncertainty Analysis Bootstrap Simulation on page 63 10 4 Variability Analysis Result Summary for All Datasets After you have reviewed or modified the selection of parametric probability distributions and parameter estimation method you can obtain a summary of the type of distribution selected parameters of the parametric probability distributions associated with each dataset the parameter estima
44. alues and the beta distribution cannot represent a dataset in which some values are outside of the range from 0 to 1 If such situations occur the AuvTool will provide a message box to suggest that users choose other distributions Note 5 The data and parametric distribution are shown in terms of cumulative probability on the Y axis versus values of the sampling dataset on the X axis Cumulative probability is the probability that a randomly selected value from the distribution will be less than or equal to the fractile of the distribution associated with the specific value of cumulative probability Note 6 On graphs that depict the origin of the X axis a spurious symbol appears at a cumulative probability of zero and an x value of zero This is not an actual data point it is an artifact of the graphics routine used at this time Note 7 Each graph depicts both the available sampling data set shown as triangular data symbols and the parametric distribution shown as a smooth line The legend of the graph indicates the sample size and the type of parametric distribution currently selected The graphical display allows you to visualize both the data and the parametric distribution Some disagreement will typically be evident 75 when comparing the distribution to the data The program gives you a capability to select from several alternative parametric distributions in most cases You can choose the one that has the best fit in your opini
45. appreciate if you would notify us of any comments you have or problems that you have encountered by sending email to Dr Chris Frey at frey eos ncsu edu and to Junyu Zheng at zhengjunyu hotmail com 119 19 0 REFERENCES Berkenpas M B et al 1998 User Manual for Integrated Environment Control Model Prepared by Carnegie Mellon University for the Federal Energy Technology Center U S Department of Energy Pittsburgh PA Bits Per Second Ltd and Pinnacle Publishing Inc 1997 The Graph Control Seattle WA Efron B 1979 Bootstrap Method Another Look at the Jackknife The Analysis of Statistics 7 1 1 26 FarPoint Technology Inc 2000 User s Guide for FarPoint s Spread 3 Morrisville NC Frey H C J Zheng 2000 User s Guide forAnalysis of Variability and Uncertainty in Emissions Estimation AUVEE Final Report Prepared by North Carolina State University for Office of Air Quality Planning and Standards U S Environmental Protection Agency Research Triangle Park NC Frey H C J Zheng Y Zhao S Li Y Zhu Technical Documentation of the AuvTool Software Tool for Analysis of Variability and Uncertainty Prepared by North Carolina State University for the U S Environmental Protection Agency Research Triangle Park NC February 2002 120
46. atistics is influenced by sample size A suggested value when the sample size is unknown but believed to be small is 5 First Parameter please see the AuvTool Conventions on page 20 for more details Second Parameter please see the AuvTool Conventions on page 20 for more details Distribution In this column you should provide the distribution type You can enter either the distribution name or the distribution code representing the distribution The following tables specifies the input for the column Table 11 1 Input Specifications for the Distribution Column Distribution Name Distribution Code Normal 0 Lognormal 1 Beta 2 Gamma 3 Weibull 4 Uniforma 5 Triangle 6 Note Distribution name is not case sensitive Estimation Method In this column enter the codes to represents the estimation method 0 stands for MoMM 1 for MLE and if you have no information for the estimation method enter 1 AuvTool will by default assign MoMM to the latter case in uncertainty analysis 11 2 Input Distribution Information from the Keyboard By following the input specifications introduced above you can input the distribution information by moving the cursor highlighted cell to a cell and then typing 59 the corresponding contents required for the cell Using the right arrow to move the cursor to the next cell at the row you are working on to get other information After finishing all inp
47. chMode Window Help 18 x Osh sae S For Help press F1 NUM AuvTool Mainframe and Main Sheet e Characterization of Variability Fitting Distributions Dataset by Dataset see page 36 e Characterization of Variability and Uncertainty Fitting Distributions by Batch Analysis see page 44 e Load Distribution Information without Original Data see page 57 e Uncertainty Analysis Bootstrap Simulation see page 63 e Fitting Distributions to the Sampling Data of the Statistics of Interests see page 72 e Variability Analysis Result Reporting see page 79 e Uncertainty Analysis Result Reporting see page 84 e Working with a Graph if desired see Working with Graph on page 100 e Working with a Sheet if desired see Working with Sheet on page 96 e Exit AuvTool see Exiting AuvTool on this page 3 3 Exiting AuvTool To exit AuvTool do one of the following e Pull down the File pull down menu or press Alt F and select Exit e Click the Close button x in the upper right hand corner of the AuvTool mainframe window or e Press Alt F4 10 4 0 INTRODUCTION TO AUVTOOL MAINFRAME MENUS In this section we will give a brief introduction to the AuvTool Mainframe Menu Commands 4 1 File Menu File New Ctrl N This command creates a new data sheet window with the default name AuvTool AuvTool prompts you to name an AuvTool file when you save it File Open Ctrl O T
48. ck the Save button in the Save as dialog box 16 5 Exporting a Sheet to a Microsoft Excel File To export a spreadsheet to a Excel file Click the right mouse button within the range of a sheet The program will popup the Working with Sheet menu Release the right button drag the pointer to Export Excel and click on it by pressing the left mouse button The program will display a Save as file dialog box with the initial file type of xls Enter a filename with an extension of xls Click the Save button in the Save as dialog box 98 Note When you save a file you can save the file to any other directory you want Just select the drive letter and the directory you want to save to in the Directories box You can also save the file to a floppy disk In order to do that just change the drive to the drive letter of your disk 99 17 0 WORKING WITH A GRAPH In this section we describe how to work with a graph including editing a graph saving a graph into a file copying a graph to other window applications and printing a graph All of these operations are the same in all modules As an example we will use the Fit a Single Distribution window in the Variability Analysis Fitting Distribution Dataset by Dataset module to help explain how to work with a graph The same procedure can be used in other modules such as the Uncertainty Analysis Bootstrap Simulation module and any other mo
49. d combo list box In this list box you can choose a color for the axes from the current color palette The same color is 104 applied to all axes The default color is automatic black or white whichever provides more contrast Position Group Variable labeled radio box When the X axis is selected in the Apply to Axis group select this option to draw the X axis intersecting the Y origin whether that is at the top bottom or middle of the graph When Y Primary is selected in the Apply to Axis group select this option to draw the primary Y axis intersecting the X origin whether that is at the left right or middle of the graph Left or Top labeled radio box When X is selected in the Apply to Axis group select this option to draw the X axis at the top of the graph regardless of the location of the Y origin When Y Primary is selected in the Apply to Axis group select this option to draw the primary Y axis at the left edge of the graph regardless of the location of the X origin Right or Bottom labeled radio box When X is selected in the Apply to Axis group select this option to draw the X axis at the bottom of the graph regardless of the location of the Y origin When Y Primary is selected in the Apply to Axis group select this option to draw the primary Y axis at the right edge of the graph regardless of the location of the X origin 105 Scale Group Zero Origin labeled radio box Select this option to draw the axes to
50. dules which have a graph 17 1 Switching between the Working with Graph Popup Menu and Graph Control Dialog Box Whenever you click the right mouse button within the range of a graph for the first time the program will popup a Working with Graph menu as shown in the window below Release the right button drag the pointer to Edit Graph click on the item by pressing the left mouse button and then click on the right mouse button again The program will popup a Graph Control dialog box shown on the next page There are four pages within the box they are the Titles page Axis page Fonts page and Design page When you click the OK or Cancel button within the Graph Control dialog box the program will exit the box However when you click the right mouse button again within the range of the graph the program will always popup the Graph Control dialog box If you want to switch to the Working with Graph popup menu for other operations 100 Fit a single distribution Go r Output Cumulative Probability Mean 0 827661 Standard Deviation 0 03 0 6 o 280126 Dataset1 Fitting Result Summary Bootstrap Popup menu for Working with Graph Graph Control x Graph Title Fitting a Distribution for Dataset 1 Bottom Title Dataset 1 Left Title Title Cumulative Probability Horizontal Up C Down Right Title Title
51. e Click Apply Now button or Ok button The difference is that the Graph Control dialog box will not exit when you click Apply Now button The graph will be automatically refreshed e If you want to abandon your font settings click the Cancel button The Graph Control dialog box will disappear and no change will be made to the fonts of a graph 115 17 3 17 4 Copying a Graph to Clipboard To copy a graph to clipboard Click the right mouse button within the range of a graph to bring up the Working with Graph menu as previously shown Release the right button and drag the pointer to Copy click on this by pressing left mouse button Now you can paste the graph to other Windows applications supporting pictures for example Microsoft Word and PowerPoint Saving a Graph to a File To save a graph to a file Click the right mouse button within the range of a graph to bring up the Working with Graph menu as previously shown Release the right button and drag the pointer to Save Click on this by pressing the left mouse button A standard Save As dialog box will pop up Enter a filename for your graph in the File Name text field in the Save As window Select one picture file type in the Save as Type combo list boxes The file will automatically be saved as a picture file We recommend that you use one of these extensions wmf jpg and bmp for the corresponding picture file formats This extension will fac
52. e sceceactaseetarcew tical sae ee ian 19 5 3 PROV TOOL Conver ton gsi siege sissy E rrp e E a cates 20 DATA ENTRY IMPORTING AND EXPORTING esessesesssooesesssecssssoossssoosse 22 6 1 Input Data from the Keyboard i ccdccsecsseesisdecchescstieviasacis eeces nacoadds 23 62 Loading Auv lool Data Fikescisisccsieissadicds eplanthatiseveciastauelerusielcaadanclacts 23 6 3 Importing Data from Other Data File Formats ec ccecceeseeeseeeteeeeees 24 6 4 Windows Copy and Paste ise fc case 2 uhachiaes otesetcoansiensGhasastesereavedeantadanceoneaes 25 6 5 Exporting Data from AuvTool Main Sheet ssoesneseesseesseseessressessessees 26 7 0 8 0 9 0 10 0 11 0 12 0 6 6 Naming a Datasctitsaca aaecscttecatoteteantiG eee a ats ctemeciom eae oaacwatae 27 Or Datatnput Checking nerangi use cchecada thease a E a ii 29 RANDOM NUMBER GENERATORS ssseeessosssoessesssocssoossoosssoesssesssoossoossosesose 30 7 1 Generating Random Samples Based on Parametric Distributions 31 7 2 Generating Random Samples Based on Empirical Distribution 31 RANDOM SEED SETTING wiissesssssesiotesssecssnssessencsessasoastnsbosossonsscnssapsabedetacsostenee 34 8 1 Using the Default Random Seeda g si03cis atte anes 34 8 2 Changing the Random Seed a ccsccssccesiscceessessrodccdecsseviecerssstiecescddemesdeadettes 35 CHARACTERIZATION OF VARIABILITY FITTING DISTRIBUTIONS DATASET BY DATASET eessssesssesssesssosssosssssssseessoos
53. e see the section on Working with a Sheet on page 96 95 16 0 WORKING WITH A SHEET In this section we describe how to work with a spreadsheet including 1 copying 1 2 printing out and pasting between AuvTool and application programs such as Exce a sheet and 3 exporting a sheet to other file formats All of these operations are the same in all modules associated with a spreadsheet As an example we will use the sheet in the Variability Analysis Fitting Distribution Summary window to help explain how to work with a sheet The same procedure can be used in other modules such as the Link Distribution module and the Batch Analysis module 16 1 Copying To copy data from a spreadsheet e Select the cells that you want to copy e Click the right mouse button within the range of a sheet The program will popup a menu as shown in the window on the next page e Release the right button drag the pointer to Copy and click on it by pressing the left mouse button 16 2 Pasting To paste data from a spreadsheet e Select the cells that you want to paste data into e Click the right mouse button within the range of a sheet The program will popup the Working with Sheet menu 96 Variability Analysis Fitting Result Summary Ioj x IV Included Variables without original data fees ae No Of Data Distribution Estimation First Second Points Type Method Parameter Parameter Fe TEA Weibu
54. e text box for a title you disable it and provide more space for the rest of the graph If you enter a title that is too long to appear in a single line the Graph Control automatically word wraps it If a title does not display at all it is because the Graph Control can not make the font small enough to fit all the text in the space provided Editing the Titles of a Graph Based on the above discussions you can enter or modify the titles of a graph When you finish your editing click the Apply Now or Ok buttons The difference is that the Graph Control dialog box will not exit when you click the Apply Now button The graph will be automatically refreshed If you want to abandon your editing click the Cancel button The Graph Control dialog box will disappear and no change will be made to the titles of a graph Note It is recommended that you do not change any setting for the Left Title group in the AuvTool You also do not need to edit the Right Title group in AuvTool 17 2 3 Editing Fonts AuvTool allows users to change the style and size of fonts for graph titles other titles labels and legend To invoke the feature first bring up the Graph Control dialog box as introduced in first section of this chapter on page 100 and then click on 112 Graph Control x Titles Axis Fonts Design Apply To Other Titles Labels C Legend Typeface __ Size v t Scal Name ria M Smart Scale
55. ed the corresponding cell will be marked as Passed If the K S test was failed it will be marked as Failed If no information is available the cell will be reported as NA AD Passed If the A D test was passed the corresponding cell will be marked as Passed If the A D test was failed it will be marked as Failed If no information is available the cell will be reported as NA 15 2 3 Switching Between the EPA SHEDS Model Format Sheet and The General Format Sheet To switch between the EPA SHEDS Model Format and the General Format select the appropriate radio button on the left top of the Summary on Uncertainties in Mean Std Deviation and Other Statistics window If the AuvTool program is displaying the EPA SHEDS format sheet click on the General Format labeled radio button The program will switch to show the sheet of the general format If the AuvTool program is displaying the general format sheet click on the EPA SHEDS Model Format labeled radio button The program will switch to show the sheet of EPA SHEDS model format 15 2 4 Exporting the Summary Tables You can export the analysis results of the sampling distribution data obtained from bootstrap simulation provided either in the sheets of the EPA SHEDS model format 94 or the general format to other file formats or to your applications You can copy save and export the both summary sheets For more information on how to do this pleas
56. eeseeseesseeseesessseseesressressessrssressessess 116 17 4 Saving a Graph to a File seeseseesseseesseessessresresseesesessseesseserssressessrssees 116 17 5 Printing a Graphoncisioronnern hiana a a a aaa 117 TROUBLESHOOTING sssesssecsssesseseseseccssesossesssecosoesosseossecoscssossesssecossssosseossses 118 REBPERENCGUS gsicessstsisveccsnscosacvivasereonteucacsavs tescensea coxooiavascss k ee ieoi ooet s nieas 120 iii 1 0 INTRODUCTION 1 1 Whatis AuvTool AuvTool is a software tool for statistical analysis of variability and uncertainty associated with fitting parametric probability distributions to data sets It was developed for the Office of Research and Development ORD of U S Environmental Protection Agency Research Triangle Park NC A technical report was written for this project with a focus on the methods and algorithms used in the AuvTool software The technical report contains a review of probabilistic analysis with detailed presentation of the methods used in the AuvTool software for fitting distributions to data uncertainty analysis and criteria for automatically selecting a best distribution model in the batch analysis The technical report also contains a case study similar to that shown here in the User s Guide and it contains results of QA AC tests The technical report is Frey H C J Zheng Y Zhao S Li Y Zhu Technical Documentation of the AuvTool Software Tool for Analysis of Variability and Uncertainty
57. first parameter 1 Parameter U The estimated first parameter for the parametric distribution describing the sampling distribution for the first or second parameter of the variability distribution 2 Parameter U The estimated second parameter for the parametric distribution describing the sampling distribution for the first or second parameter of the variability distribution 2 Parameter V The estimated second parameter in the case of a parametric distribution for the distribution representing variability Uncertainty Dist For 2 Para The parametric distribution type describing the sampling distribution data for the estimated second parameter 3 or 4 Parameter V or U not available for the current version of AuvTool Note For the definitions of 1 parameter and 2 parameter please refer to the section on AuvTool Convention on page 18 15 2 2 Brief Explanation of Columns inside the Sheet of General Format As shown in the following four figures the general format presents three parts of the analysis results The first part shows the distribution information used to describe the presented by default The second part shows the goodness of fit statistical test results for 90 Summary on uncertainties in mean std deviation and other statistics C EPA SHEDS Model Format General Format Dataset 1 Ea Dataset 2 ae EA Dataset 3 F Dataset 4 8 Dataset 5
58. g Distribution labeled tab page The program will go to the Fitting Uncertainty Sampling Distribution page which is shown on the next page This module provides two different parameter estimation methods MoMM and MLE This module allows you to visualize your own selection of parametric distributions in comparison to actual data and presents the K S test and Anderson Darling test results to help you choose a good fit 72 Number of Sampling data Dataset combo list box to select a dataset The size of sampling data which is the same as the bootstrap replication number for the chosen dataset K S test information Bootstrap Simulati Bootstrap Simi rm Input m Statistic Data Sets m K S Test Dataset 1 a i Sampling Size ooseeo7 252081 Critical Valu ft 0 05 Fitted Distribution Significant L4 tel 0 039623124 612963 Legnermal Statistics of Interest Mean ha Distribution Type N Auto Estimation Method Distribution Type combo box Auto is not a distribution type but an option which can allow the program to automatically choose a good distribution type Passed or Not Passed m Anderson Darling Test Value fi 11152279022898 Critical Value at 1 05 Significant Leva 0 752 ilative Probability Method Of Mame Max Likelihool Estimation Results Mean 0 8246061 896 Standard Dg 0 075061
59. haracterization of Variability and Uncertainty Batch Analysis on page 44 4 6 Window Menu The Window menu contains window management commands At the bottom of this menu all currently opened child window are listed Window Cascade This command rearranges all open sheet plot windows in overlapping layers The title of each window is revealed so that you can see the name of the sheet plot it contains Window Tile This command displays all open sheet plot windows without overlapping them When possible the windows are all given equal room on the screen Window Arrange Icon After several open sheet plot windows are minimized as icons in the main window this command can quickly place the icons in neat rows along the bottom of the screen 4 7 Help Menu Help Help Topics This command will pop up AuvTool online help documentation dialog box Help About AuvTool This command will display the version information about AuvTool 17 5 0 PROBABILITY DISTRIBUTION DEFINITIONS AND AUVTOOL CONVENTIONS In this section definitions of probability distributions used in the AuvTool are presented The conventions used in the AuvTool are also introduced 5 1 Definitions of Parametric Probability Distributions Commonly used parametric distributions used in variability and uncertainty analysis include normal lognormal Weibull gamma beta uniform and triangle distributions Table 5 1 lists the definitions for the seven common
60. his displays a standard Open File dialog box with the default file search extension ss3 You can use this command to open an existing data file saved by AuvTool The following options allow you to specify which file to open File Name Type or select the filename you want to open This box lists files with the extension you select in the List Files of Type box List Files of Type Select the type of file you want to open ss3 Drives Select the drive in which AuvTool stores the file that you want to open Directories Select the directory in which AuvTool stores the file that you want to open Once you have typed a proper filename in the File Name edit box choose the OK to open the file you specified 11 Note Before you open an existing file you need to first open an empty sheet by clicking the File New command File Close This command lets you close the current active datasheet File Import Excel The File Import Excel menu item displays an Open File dialog box with the default file search extension xls You can use this command to open an existing Microsoft Excel 97 file format data You should specify a file to open by clicking on it or inputting the file name File Import Tab Delimited The File Import Tab Delimited menu item displays an Open File dialog box with the default file search extension txt You can use this command to open a data file which is saved with
61. hown in terms of cumulative probability on the Y axis versus values of the dataset or a variable on the X axis Cumulative probability is the probability that a randomly selected sample within the variable will have a value less than or equal to the associated value of the variable on the X axis Note 5 On graphs that depict the origin of the X axis a spurious symbol appears at a cumulative probability of zero and an x value of zero This is not an actual data point it is an artifact of the graphics routine used at this time Note 6 Each graph depicts both the available data set shown as triangular data symbols and the parametric distribution shown as a smooth line The legend of the graph indicates the number of data points available and the type of parametric distribution currently selected The graphical display allows you to visualize both the data and the parametric distribution Some disagreement will typically be evident when comparing the distribution to the data The program gives you a capability to select from several alternative parametric distributions in most cases You can choose the one that has the best fit in your opinion Note 7 If you want to edit a graph save a graph as a file or print a graph out please see the section Working with a Graph on page 100 9 1 Selecting a Dataset If you have multiple datasets to analyze you should select a dataset as a current dataset and then analyze it as shown below
62. ilitate later insertion of the picture file into a MS Word document 116 Note There are tree kinds of picture file types available you can save as in the AuvTool They are wmf jpg and bmp file format types e Click the Save button in the Save As window to save the file 17 5 Printing a Graph To print a graph e Click the right mouse button within the range of a graph to bring up the Working with Graph menu as previously shown e Release the right button and drag the pointer to print Click on this by pressing the left mouse button The program will print the graph 117 18 0 TROUBLESHOOTING This is the first version of the AuvTool program Although it has been tested it is possible that you may encounter difficulties Due to potential instability of numerical simulations in some cases especially for the beta distribution bootstrap simulation may take a long time or may not go to completion Although the program provides some error handling there maybe some unknown fatal errors which occur in few cases The following will introduce the possible errors that might happen and the methods to deal with them Problem The program stops working after you do a bootstrap simulation for a dataset the reason is often because of the appearance of a fatal mathematical error In this case it will be necessary to end program use and start over Solution Press CTRL ALT DELETE keys together A dialog box will appear
63. imal Solution for MLE Uniform y N A Sy OTST y y Optimal Solution for MLE Triangle Note V The method is available for the given distribution A The plotting method is used instead of MOMM for Weibull distribution N A The method is not available in this case Table 9 2 Goodness of fit Test Method Availability for Probability Distributions Distribution Types Kolmogorov Siminov Test Anderson Darling Test Normal N N Lognormal Beta Gamma Weibull N N N Uniform Triangle a jee Note N The test is available for the given distribution Note 3 For some datasets some distributions cannot be used to fit them For example lognormal gamma and Weibull distributions cannot be used to describe datasets in which there are some negative values and a beta distribution cannot represent a dataset in which some values are outside of the range between 0 and 1 If such situations occur AuvTool will provide a message box to suggest that users choose other distributions However in some cases the normal distribution might be chosen by a user or the automatic batch fit process to represent a dataset that must be non negative Because the program does not know which datasets must be 38 non negative it is the user s responsibility to make sure that the normal distribution is not used inappropriately Note 4 The data and parametric distributions are s
64. iminates the need to master the underlying commands normally required in the DOS environment Graphic Control Server 5 0A provides graphic presentation of calculation results Far Point Spread 3 0 provides a spreadsheet for data entry and outputs of results Visual C runtime libraries and the dynamic link libraries and runtime libraries of Graphic Control Server 5 0A and Spread 3 0 are included with the AuvTool installation package and do not need to be licensed separately 1 5 Using Online Help Documentation The online help provides an online version of this User s Guide and of the Technical Documentation for Analysis of Variability and Uncertainty for the AuvTool Software via a Windows Help System You can access the AuvTool help files by doing any one of the following when you are running AuvTool e Press F1 key e Pull down the Help menu at the top of the AuvTool window select Help Topics e Click the Help Topics on the toolbar on the left side of the AuvTool Window The AuvTool Help File System will display Help Topics AuvTool Online Help Documentations _2 x Contents Index Find Click a book and then click Open Or click another tab such as Index Introduction to Menus w Technical Documentations Visualizing Data Using Empirical Distribution and Scatter Plots Definitions of Parameteric Distributions oS Parameter Estimation of Probability Distributions oS Sampling Algorithms for Parametric Distributions res G
65. ink Distributions module by pulling down the Batch Mode pull down menu and selecting Link Distributions The program will display the Link the Distribution Information of Variables without the Original Data dialog box shown on the next page You can provide the distribution information via four ways You can enter information by keyboard load data from an existing AuvTool disk file import data from other file formats or use the Window copy and paste command to provide the necessary information 57 Link the distribution information of variables without the original data Variable Name Sample Size First Second Distribution Parameter Parameter Estimation Method Link Distribution Information Cancel Link Distribution sheet Note 1 Each row represents the distribution information for one variable 11 1 Brief Explanation of Input Specification of Columns There are six columns in the Link Distribution sheet The input specification for each column is introduced as follows Variable Name In this column you can specify any name for the variables you are analyzing There is no limit for your variable name length Sample Size In this column you should provide the number of data points for the original data for the known distribution In some cases you might not have such information However you may also enter any value for sample size you wish to explore how the range of uncertainty in selected 58 st
66. ion combo list box to select a distribution Number of data points Cumulative Probability itting Result Summary Bootstrap 7 Normal K S test information 0 258 Passed or Not Passed m nderson Darling Test Value 0 158062250395989 Critical Value at 0 05 SignificanyLevel 0 752 Passed Type of parametric distribution fitted to dataset Anderson Darling test information Parameter Estimation Methods Parameter estimates estimation method When you invoke the module as shown in the following figure the program will by default analyze the first dataset and show its fitting results Note 2 For some distribution types the MLE or MoMM estimation methods and the Anderson Darling test are not available Table 9 1 summarizes the availability of MoMM and MLE for probability distributions used in the AuvTool Table 9 2 summarizes the Kolmogorov Smirnov K S and Anderson Darling A D test method availability for probability distributions used in AuvTool 37 Table 9 1 Parameter Estimation Method Availability for Probability Distributions Distribution MoMM MLE Comments Types Normal y y Analytic solution for MLE Lognormal y y Analytic solution for MLE Beta y y Optimal Solution for MLE Gamma y y Optimal Solution for MLE Weibull A y Opt
67. ion to 53 accomplish these tasks By simply invoking the feature the program will do batch bootstrap simulation for all datasets inside the Batch Analysis Data and Property Sheet automatically find the best parametric probability distribution model to fit to the statistics of interest for all datasets and report the analysis results To do this Select the parameter estimation method for the sampling distribution by clicking one of two radio boxes on the right bottom corner of the Batching Fitting window The program will set MoMM as the default parameter estimation method Enter the replication number which refers to of the number of bootstrap sample that will be simulated for bootstrap simulations The program sets 200 as the default number However larger values will give more numerically stable results at the expense of longer run time Click the Uncertainty Sampling Summary button on the right bottom corner of the Batching Fitting window The program will display the Summary on the Fitted Distributions to the Statistics of Interest dialog box More information on the summary can be found in the Uncertainty Analysis Result Reporting on page 84 WARNING The user of AuvTool is cautioned that the availability of a batch mode technique for choosing a distribution based upon the K S test is not a substitute for the use of judgment The K S test is based upon a specific criterion which may or may not be importa
68. is M 3D I Fonts M Markers M Trends M Overlay M EnorBar M B ground M System Help I About M Legend M Labels Property Pages Toolbar Cancel Apply Now Help Design page within the Graph Control dialog box e Uncheck the Run Time on Right Click labeled check box in the Property Pages group by clicking on it e Click the OK button at the bottom of the Graph Control dialog box to exit the box e Click the right mouse button and the program will popup the Working with Graph menu as previously shown You can return to the Graph 102 Control dialog box as introduced at the beginning of this subsection or you can go to other options for saving copying and printing a graph Note You do not need to modify other control options in the Design page within the Graph Control dialog box and you do not need to use other options provided in the Design page Therefore no detail is provided here regarding the Design page 17 2 Editing a Graph You can edit an AuvTool graph by changing the scale of an axis titles of the graph and fonts for displaying the titles and legends 17 2 1 Editing Axes By using the editing axes feature you can edit the axes of a graph including changing the scale of axes changing the number of tick marks and changing the display of axes To invoke the feature first bring up the Graph Control dialog box as introduced above and then click on the Axis tab to e
69. is example we load an AuvTool file The file is an example used to analyze variables without original data in the Batch Analysis and other modules The user can find this file in the working directory of AuvTool Note 2 After you load the distribution files for the variables without original data you can do uncertainty analysis for these variables in the Batch Analysis module However you need to exit the Link Distribution module before you do further analysis Note 3 For any operations on the sheet please see Working with a Sheet on page 96 Link the distribution information of variables without the original data First Second Estimation E Variable Name Sample Size Distribution Metos EA NoData Name 1 15 Normal NoData Name 2 20 1 EA NoData Name 3 25 Gamma 61 11 4 Exiting the Module You have two ways to exit the Fitting Distribution module If you want to load the distribution information for uncertainty analysis click the OK button in the window The program will automatically link the information to other modules This information will be used in the Batch Analysis and Uncertainty Analysis modules If you do not want to load the distribution information for further analysis just click the Cancel button The program will exit the window without passing any information to other modules 62 12 0 UNCERTAINTY ANALYSIS BOOTSTRAP SIMULATION In this section you will learn
70. iven for the variables you analyzed No of Data The number of data points for each data set is given Distribution Type The distribution type used to represent the variability for the corresponding variable or data set is shown Estimation Method The parameter estimation method used to estimate the parameters for the bootstrap samples is given either MLE or MoMM Mean 2 5 Percentile The 2 5 percentile of the sampling distribution of the mean is given This is the lower bound on the 95 percent confidence interval for the mean 85 Mean Mean The mean of the sampling distribution of the mean is given Mean 97 5 Percentile The 97 5 percentile of the sampling distribution of the mean is given This is the upper bound on the 95 percent confidence interval for the mean Standard Deviation 2 5 Percentile The 2 5 percentile of the sampling distribution of the standard deviation is given This is the lower bound on the 95 percent confidence interval for the standard deviation Standard Deviation Mean The mean of the sampling distribution of the standard deviation is given Standard Deviation 97 5 Percentile The 97 5 percentile of the sampling distribution of the standard deviation is given This is the upper bound on the 95 percent confidence interval for the standard deviation 15 1 2 Exporting The Uncertainty Analysis Summary Table You can export the uncertainty analysis results to other file formats or to other a
71. ked the status bar will not be displayed 15 4 4 Uncertainty Menu Uncertainty Random Seed Setting This command will popup a dialog which allows users to set the random setting See Random Seed Setting on page 34 for more details Uncertainty Random Generator This command will popup a dialog which allows users to generate random numbers from normal lognormal gamma beta Weibull uniform symmetric triangle and empirical distributions For more details see Random Number Generator on page 30 Uncertainty Single Distributions This command will popup a dialog box which allows users to estimate parameters for normal lognormal gamma beta Weibull uniform symmetric triangle distributions single dataset by single dataset For more details see Characterization of Variability Fitting Distribution Dataset by Dataset on page 36 4 5 Batch Mode Menu Batch Mode Load Distributions This command will popup a dialog which allows users to load or enter existing distribution information that users have for batch uncertainty analysis For more details see Enter or Load Distribution Information on page 57 Batch Mode Batch Analysis This command will popup a dialog which allows users to do batch variability and uncertainty analysis for their datasets It includes parameter estimation bootstrap 16 simulation automatic best distribution selection and so on For more details see C
72. l include two types of file formats Excel and Tab Delimited text files Note Even if users do not choose to output the simulation results to files here they still can save the analysis results after the Summary on Uncertainties in mean std Deviation and other statistics window shows up Users can export the analysis results through the methods discussed in the section on Working with Sheet on page 96 87 Output to files Ea Do not output the results to file Qutput the simulation results to files Directory C WAuyT ool_ vers Cancel Output to files Dialog After the Output to files dialog box disappears it may take a while to get the reports The time involved depends on the speeds of your computer the number of data sets you are analyzing which parameter estimation method is used and the bootstrap simulation parameters When all relevant calculations are done the program will display the Summary on Uncertainties in Mean Std Deviation and Other Statistics window Inside the window there are two kinds of sheets One presents the analysis results on the sampling distribution data especially for EPA SHEDS model use another contains the results in a general format By default the program will show the sheet for the EPA SHEDS model format 15 2 1 Brief Explanation of Columns inside the Sheet of EPA SHEDS Model Format As shown in the two figures on the next page the main columns are
73. layed in the header of the column ig AuvTool AuyToo1 lej x G Eie Edit View Uncertainty BatchMode Window Help lel x Oe S 2 08600637 0 8600537 0 8600537 0 8600537 0 6599163 0 7957628 0 7957828 0 7957828 0 7957828 0 5754917 0 572737 05727397 0 5727397 0 887456 o g100306 0 9100906 0 9100906 0 9100906 07290770 1 2397860 1 2397850 1 2397850 1 2397850 1 2572018 1 0280496 1 0280496 1 0280496 1 0280496 0 903735 10821564 1 0821564 1 0821564 1 0821564 0 9892824 07679276 0 7679276 0 7679276 0 7679276 05404633 05773983 0 5773989 05773969 0 573989 0 269602 014426231 0 4426231 0 4426231 0 4426231 0 2046598 1 0643828 1 0643828 1 0643828 05592417 0 5592417 0 5592417 0 4770342 0 470342 0 4770342 08723086 0 8723096 0 872309 31210067 3 1210067 3 121067 1 0486513 1 0466513 1 0486513 1 2443522 1 2443522 1 244352 1 037618 1 0237618 1 0237618 14 7555076 1 7555076 1 7555076 21814990 21814990 21814990 0 7480611 0 7480611 0 6669520 0 6669520 1 1089564 1 1089564 0 6238788 0 6238788 1 9628555 1 962855 1 0434862 1 0434862 1 8293716 1 8293716 1 6648288 1 6648288 0 727116 0 727116 1 1605744 1 1605744 0 795921 0 795921 0 8954526 0 954526 2 2244581 22244581 0 9267319 0 9267319 1 129726 1 129726 0 5535690 0 5535690 For Help press F1 NUM Note 1 When the titles or name of datasets are located in the headers of columns The first row is title row labeled check box must be disabled 28 Note 2 Au
74. ll Moment 0 91730 3 73194 Loqnorm g 0 54696 Lognorm 1336 0 50263 Lognorm 2989 0 47275 Normal 0 33035 Export Tab Te Export Excel Popup menu for working with sheet Popup menu for working with sheet e Release the right button drag the pointer to Paste and click on it by pressing the left mouse button 16 3 Printing a Sheet To print out a spreadsheet e Click the right mouse button within the range of a sheet The program will popup the Working with Sheet menu e Release the right button drag the pointer to Print and click on it by pressing the left mouse button Note The AuvTool does not provide a strong feature of formatted printing You might not be satisfied with the format of output when you printed directly from AuvTool If you need more advanced print features we recommend that you 97 export the AuvTool spreadsheet results to Microsoft Excel where you can have more control over the format 16 4 Exporting a Sheet to Tab Delimited Text File To export a spreadsheet to a tab delimited text file Click the right mouse button within the range of a sheet The program will popup the Working with Sheet menu Release the right button drag the pointer to Export Tab Delimited and click on it by pressing the left mouse button The program will display a Save as file dialog box with the initial file type of txt Enter a filename with an extension of txt Cli
75. must name each dataset You can refer to the Naming a Dataset section on page section 27 for how to name a dataset 6 2 Loading AuvTool Data File AuvTool has its own data file format with an extension of ss3 or SS3 It is in a binary format To open an existing AuvTool data sheet file 23 e Pull down the File pull down menu or press Alt F and select Open or just click the Open icon on the tool bar The program will display an Open file dialog box as shown below Em AuvTool AuvToo1 a x H File Edit View Uncertainty BatchMode Window Help x AERLE Look in Samoe fa c a testCase_excelCopy ss3 a testData ss3 a testExcel_1 ss3 a TestFile ss3 a testFile_1 ss3 a testCase_copy ss3 a WINDOWSDesktopss ss3 File name wINDOWSDesktopss ss3 Open Files of type ssa Files ss3 z Cancel e Find the file name that you would like to open Click the Open button in the Open dialog box The AuvTool main sheet will load your data Now you can use any features that AuvTool provides 6 3 Importing Data from Other Data File Formats AuvTool can also exchange data with many popular data file formats such as Microsoft Excel files XLS and Tab Delimited files provided by any text editor Since the AuvTool data sheet can only handle numerical value and text string only for the first row when used as a title of a dataset when you import data into AuvTool m
76. n at the bottom of the Fit a Single Distribution window or by clicking on the Fitting Distribution Summary button at the left bottom of the Batch Fitting window When you click on either of them the program will display the following Variability Analysis Fitting Distribution Summary window If checked the summary table will include the distribution information for those datasets without original ig Weibull Moment 0 91730 3 73194 ma een Lognormal Moment 0 07159 0 54696 3 Lognormal Moment 0 11336 0 50263 1000 Lognormal Moment 0 12989 0 47275 10 Normal Moment 0 65092 0 33035 OK Cancel Variability Analysis Fitting Distribution Summary window 1 The program by default will only display the fitting result information for those variables with original data However if desired users can also display the distribution information for variables without original data by clicking on the check box within the 79 Variability Analysis Fitting Result Summary Ioj Xx T Included Variables without original data First Second KS Test Anderson KS Test AD test Parameter Parameter Darling Test Passed or Not Passed or Not 3 73194 0 13717 0 162180 Passed Passed 0 54696 0 14786 0 465020 Passed Passed 0 50263 0 09052 0 317267 Passed Passed 0 47275 0 01583 0 306336 Passed Passed 0 33035 0 13662 0 205622 Passed Passed Cancel Variability Analysis Fitting Distribution Summary window 2
77. n enter the module by pulling down the Batch Mode pull down menu in the AuvTool Mainframe window and selecting Batch Analysis The program will display the above Batch Fitting dialog box 44 Click here to graphically show the goodness of the fit to the selected dataset These datasets have original data the information is from AuvTool Main Sheet The number of bootstrap samples Distribution Estimation Bootstrap Choice Method Comparision Simulation Show ShowAll_ Bootstrap Show ShowAll Bootstrap Show ShowAll_ Bootstrap Show ShowAll_ Bootstrap Show ShowAll_ Bootstrap Show ShowAll Bootstrap Show ShowAll Bootstrap Show Showall Bootstrap a as f rd a Method of Matching Moment Save Fitting Result 9 Batch Bootstrap Load Uncertainty Result Batch Fitting 2 Uncertainty Saml Mar Likelihood Estimation 7 Batch Analsyis for Uncertainty Sampling Distribution Those variables do not have original data The information is from the Link Distribution module If checked the original data is available for this variable The Batch Analysis module is more powerful than the Fitting Distribution Dataset by Dataset module previously introduced It includes all features implemented in the Fitting Distribu
78. n in the Save as dialog box 10 7 Loading the Existing Batch Analysis Data and Property Sheet You can load the files describing the batch analysis information back to the Batch Analysis Data and Property Sheet However before you can do any further analysis you also need to load the file containing the corresponding original datasets into the AuvTool main sheet If there exists some cases without the original data in the Batch Analysis Data and Property Sheet you also need to link the distribution information file to the Link Distribution module To load the Existing Batch Analysis Data and Property Sheet e Click the Load button on the left bottom corner of Batch Fitting window e The program will display an Open file dialog box e Choose the file name you want to load click the Open button in the Open dialog box 10 8 Automatic Batch Analysis of the Sampling Distribution Data for Statistics of Interest AuvTool not only provides a summary of uncertainty in the mean and standard deviation but also includes a feature which allows users to do further analysis regarding the sampling distribution data from bootstrap simulation for selected statistics of interest This feature enables users to fit a parametric probability distribution to the simulated data for the sampling distribution of the mean standard deviation and distribution parameters In the Batch Analysis module the program provides an automatic batch calculat
79. nable the Axis page which is shown on the next page Introduction to the Controls within the Axis Page The Axis page has several groups of input fields in a variety of formats These groups include 1 Apply to Axis at the top of the page 2 Position at the left side under the Apply to Axis group 3 Scale next to the Position group near the center of the page 4 Range next to the Scale group on the right senter of the page 5 103 Graph Control x Apply to Axi pply to Axis Color of Axes xX YPrimay Y Overlay Z Ez Position Scale Range Variable Zero Origin Max fi Left Variable Origin Min jo Right User Defined Ticks E Tick Marks Grids V Show Through Axes T Show Eyer fi 4 ave Inside Axes Style Minor jo 4 C Dutside Axes Color H ae Cancel Apply Now Help Axis page within Graph Control dialog Tick Marks on the lower left hand position of the page and 6 Grids on the lower right hand position of the page Each of these groups is described in detail Apply to Axis Group X labeled radio box Select this option to view and or change the settings for the X axis Y Primary labeled radio box Select this option to view and or change the settings for the Y axis there is the only one Y axis when you do not have an overlay graph Color of Axes labele
80. nitions please see the section of Probability Distribution Definitions and AuvTool Conventions on opage 20 Note 2 For information on how to save or export the sampling results please see Working with a Sheet on page 96 7 1 Generating Random Samples Based on Parametric Distributions To generate random samples e Specify the distribution type enter the first and second parameters and specify the number of samples e Click Generate button the sampling results will be displayed in the first column of the sheet Note 1 If you find that there are not sufficient significant figures in reporting results for small numbers check the Scientific Notation labeled checkbox by clicking on it The program will report the results in scientific format 7 2 Generating Random Samples Based on Empirical Distribution AuvTool has a feature to generate random samples based on an empirical distribution To generate random samples based on an empirical distribution e Pull down the Distribution Type combo box in the Random Sample Generator dialog box and select Empirical Distribution The program will 31 prompt you to enter your dataset into the first column of the data sheet The Random Sample Generator dialog box will become e Enter your dataset into the first column of the sheet labeled A as shown in the above figure e Click the Generate button The sampling results will be displayed in the
81. nt to a particular analyst or decision maker in the 54 context of a specific problem The K S test does not screen for results that may be physically implausible such as a probability of sampling negative values for a quantity that must be non negative The appropriateness of selection of a distribution depends on the data quality objective of each analysis which may differ from one situation to another Therefore uncritical application of the batch mode feature of AuvTool for seeking a best fit distribution is likely to lead to inappropriate selection of a probability distribution model in some cases It is the user s responsibility to evaluate the automatically selected parametric probability distribution for appropriateness with respect to the user s own criteria and needs Note 1 In the automatic batch analysis the program assumes that the replication number number of bootstrap samples of the bootstrap simulation for all datasets is the same and that the number of sample for estimating the variability for each alternative frequency distribution is the same as the replication number Note 2 Recommended that values for the replication number of the bootstrap simulation are from 200 to 2000 Note 3 The program provides a module which allows users to select parametric distributions to fit to the sampling data for the statistics of interests For more information please see the Uncertainty Analysis Bootstrap Simulation module
82. odify the distribution type However for those cases which do have original data users can modify the option and subjectively select the distribution type they want to fit Note 4 In the column of Estimation Method for those cases which do not have original data users cannot modify the parameter estimation method If users do not have any information on the estimation method for some of those cases the rows on the batch analysis data and property sheet will display as NA However in uncertainty analysis the program will by default assign MoMM to these cases For those cases which have original data users can freely select the parameter estimation method Note 5 The Visual comparison feature is not available for those cases which do not have original data 47 10 1 Showing a Graph of the Fitted Distribution for a Chosen Dataset In the Batch Analysis module AuvTool has a feature to let the user visualize the fitted distribution in comparison to a dataset To show a graph of the fitted distribution for a chosen dataset e Click the Graph button on the row of the dataset you want to choose e The program will display the fitting result and graph in the Fitted Distribution to the Selected Dataset dialog box If the dataset you select has original data the dialog box will look like the figure on the next page Fitted Distribution to the selected dataset OP x r Status r Statistical Tests
83. of the parametric probability distribution models or with the interpretation or the values of the parameters in order to use this program Introduction to the Example Used in the User s Guide In the User s Guide we use an example study to help describe the use of the AuvTool The example datasets shown in the all pictures in the Guide come from the example study In the example study there are five datasets with original data which are named as Dataset 1 Dataset 2 Dataset 3 Dataset 4 and Dataset 5 20 respectively and three datasets without original data which are named as NoDataName 1 NoDataName 2 and NoDataName 3 respectively These datasets are included in two files which are called Example WithData ss3 and ExampleWithoutData ss3 repectively The two files are contained in the installation package of AuvTool During the process of installing AuvTool the setup program will automatically copy the two files to the working directory of AuvTool You can find these two files in this directory 21 6 0 DATA ENTRY IMPORTING AND EXPORTING In this section you will learn how to enter data in the AuvTool data Main Sheet for variability and uncertainty analysis and how to import or export data through AuvTool Before you can do any analysis using AuvTool you must provide data to the Main Sheet in the AuvTool mainframe window as shown in the following
84. on Note 8 If you want to edit a graph save a graph as a file or print a graph out please see the section Working with a Graph on page 100 13 1 Fitting a Distribution for a Statistic To fit a parametric distribution to a sampling distribution data set for a selected statistic e Select a dataset by pulling down the Data Sets labeled combo list box menu on the top left corner position of the Fitting Uncertainty Sampling Distribution page and click on the dataset name you want to choose The program will update the information of the Sampling Size labeled box and the Fitted Distribution labeled edit boxes for the corresponding dataset you chose e Select a statistic of interest by pulling down the Statistics of Interest labeled combo list box menu on the left side of the module as shown below Statistics of Interest Mean x Standard Deviation First Parameter Second Parameter e Select a distribution to fit to the sampling distribution data for the chosen statistic by pulling down the Distribution Type labeled combo list box menu on the left side of the module as shown below 76 Distribution Type e Select an estimation method in the Estimation Method radio box group by clicking on one of them e Click the Go Fit button to fit the chosen distribution to the sampling distribution data for the statistic of your chosen dataset using the estimation method you chose The graph will be updated au
85. oodness of Fit of Probability Distribution Models res Characterization of Variability and Uncertainty Using Parametric Distrik es References oS AuyT ool User s Guide Close Print Cancel The AuvTool Online Help Documentation Window 1 6 Disclaimer of Warranties and Limitation of Liabilities This report was prepared by the Computational Laboratory for Energy Air and Risk located in the Department of Civil Engineering at North Carolina State University as an account of work sponsored by the U S Environmental Protection Agency Office of Research and Development Research Triangle Park NC under contract No ID S794 NTEX This paper has not been subject to any EPA review Therefore it does not necessarily reflect the views of the Agency and no official endorsement should be inferred The opinions findings and conclusions expressed represent those of the authors and not necessarily the EPA Any mention of company or product names does not constitute an endorsement by the EPA NEITHER ANY MEMBER OF EPA ANY COSPONSOR THE ORGANIZATION S NAMED BELOW NOR ANY PERSON ACTING ON BEHALF OF THEM A MAKES ANY WARRANTY OR REPRESENTATION WHATSOEVER EXPRESS OR IMPLIED I WITH RESPECT TO THE USE OF ANY INFORMATION APPARATUS METHOD PROCESS OR SIMILAR ITEM DISCLOSED IN THIS REPORT INCLUDING MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE OR II THAT SUCH USE DOES NOT INFRINGE ON OR INTERFERE WITH PRIVATELY OWNED RIGHTS INCLUDIN
86. parametric distributions included in AuvTool Table 5 1 Definitions of Probability Distribution Density Function for Parametric Distribution in Included in AuvTool Name of ait Distribution Probability Density Function PDF ees Normal f x e 2 21o 1 Inx p Lognormal f x e 0 lt x lt 0 x20 a l y B 1 Beta f x I x 0 lt x lt 1 B a a B 1 an x B Gamma f x 8 eis 0 lt x lt o Ta Weibull f x To 9 exp x k 0 lt x lt w Uniform f x a lt x lt b b a Symmetric b x a Triangle F x b a b lt x lt a b In the Table 5 1 for the normal distribution u is the arithmetic mean and o is the arithmetic standard deviation For the lognormal distribution nx is the mean of n x and Opx is the standard deviation of n x In the beta distribution a and B are shape parameters and B a B is the beta function For the gamma distribution a is the shape parameter P is the scale parameter and I is the gamma function For the Weibull distribution k is the scale parameter and c is the shape parameter For the uniform distribution a and b are the smallest and largest possible values For the symmetric triangle distributions a and b determine the range that a variable can vary 5 2 Empirical Distribution An empirical distribution can be defined as a discrete distribution F that gives equal probability 1 n to each
87. pe labeled edit box and the one in the current the estimation method labeled edit box for the selected dataset 65 Change the bootstrap simulation parameters as introduced above if desired Click the Go button on the left bottom corner of the Bootstrap Simulation Graph page The display will be updated to show the probability bands of the fitted distribution or uncertainty estimate of the statistics you chose for your selected dataset It might take some time to get the results which depends on the speed of your computer the parameter estimation method used for the selected dataset and the values you choose for the bootstrap simulation parameters In rare cases if you use MLE for beta gamma and the Weibull distributions and if the delay seems too long it could be because of a failure of the nonlinear optimization method If this situation occurs please see the Troubleshooting section on page 118 12 2 Brief Explanation of the Graphical Displays The graphical results available in the Bootstrap Simulation Graph page are of two main types 1 Probability Band Shown here are 50 percent 90 percent and 95 percent probability bands for the parametric distribution fitted to the dataset for the currently selected variable The method by which the probability bands are calculated is described in the accompanying technical manual These probability bands depict a plausible range which may enclose the true but
88. pears centered at the bottom of the graphing window A bottom title frequently explains the X axis Left Title group often used to explains the Y Axis 110 The Title edit box lets you enter text for the left title which can be up to 80 characters in length Horizontal labeled radio box Elect this option if you want the title to print horizontally Up labeled radio box Select this option if you want the title to print vertically running in an upward direction In AuvTool this is default option Down labeled radio box Select this option if you want the title to print vertically running in a downward direction Right Title group The Title edit box lets you enter text for the right title which can be up to 80 characters in length The right title frequently explains the right hand Y axis when you have an overlay graph Horizontal labeled radio box Select this option if you want the title to print horizontally Up labeled radio box Select this option if you want the title to print vertically running in an upward direction In AuvTool it is default option Down labeled radio box Select this option if you want the title to print vertically running in a downward direction Note When you enter text for a title the Graph Control adjusts the rest of the graph window to provide space either by redrawing the graph and associated objects at a 111 smaller size or by decreasing the space between objects When you clear th
89. pop up menu or a sub menu which contains two commands These commands let you insert one blank column and one blank row Column This command inserts a blank column at the current cursor column position 14 Row This command inserts a blank row at the current cursor row position Edit Delete The Edit Delete command works like the Edit Clear command It removes the selected data from the data sheet but does not place it into the Clipboard This menu item has also a pop up menu or a sub menu which contains two commands These commands let you delete one blank column and one blank row Column This command deletes a blank column at the current cursor column position Row This command deletes a blank row at the current cursor row position This command also shifts the data sheet so that there are no blank cells Edit Clear The Edit Clear command removes the selected data from the data sheet but does not place it into the Clipboard The removed data cells are filled with blank cells This means that you can not paste the data as you could if you had chosen Cut or Copy commands 4 3 View Menu View Toolbar This command controls the display of toolbar within the main window frame If checked it will display the toolbar If not checked the toolbar will not be displayed View Status Bar This command controls the display of status bar within the main window frame If checked it will display the status bar If not chec
90. pplications You can copy save and export the uncertainty analysis results summary sheet For more information on how to do this please see the section on Working with a Sheet on page 96 86 15 2 Reporting the Summary of the Fitted Parametric Distributions to Sampling Distribution Data for Statistics of Interest You can get summary reports for the results of fitting parametric distribution to sampling distribution data for statistics of interest by clicking on the Uncertainty Sampling Summary button on the right bottom of the Batch Fitting window or by clicking on the Uncertainty Distribution Summary button on the right bottom corner of the Fitting Uncertainty Sampling Distribution page of the Bootstrap Simulation window Before the program will display the Summary on Uncertainties in Mean Std Deviation and Other Statistics window first it will popup an Output to files dialog box to prompt users as to whether the simulation results will be output to files By default the program assumes that users are not planning to output the analysis results to files here If users want to output the results to files select the output the simulation results to files labeled radio box by clicking on it and enter the directory and file names that the analysis results will be output to The program will automatically save the analysis results in the format of the EPA SHEDS model to the files after the simulations are finished The files wil
91. re please see the Characterization of Variability and Uncertainty Batch Analysis module on page 44 You enter the Characterization of Variability Fitting Distributions Dataset by Dataset module by pulling down the Uncertainty pull down menu and selecting Single Distribution The program will display the Fit a Single Distribution dialog box shown on the next page This module allows you to select a dataset to analyze and to select parametric distributions to fit a dataset or to use an empirical distribution to describe a dataset This module provides two different parameter estimation methods Method of Matching Moment MoMM and Maximum Likelihood Estimation MLE for you to choose This module allows you to visualize your selection of parametric distributions in comparison to the actual data and presents the K S test and Anderson Darling test results to help you choose a good fit The decisions made via the module provide a basis for uncertainty analysis Note 1 Initially AuvTool assigns a default normal distribution to all datasets listed in the dataset list combo box and sets MoMM as the default parameter 36 Dataset combo list box to select a dataset Fit a single dis Input Data Sets Dataset 1 Distribution Type Estimation Method Normal kd Method OF Moment C Max Lik ihood Method Output Mean 0 827661 Standarq Deviation Distribut
92. reset the Using Default Random Seed labeled checkbox by simply clicking on the checkbox 34 8 2 Changing the Random Seed To change the random seed e Invoke the Random Seed Setting module as introduced above e Click on the Using default Random Seed labeled checkbox to remove the check mode e Enter one large number into the Set Seed labeled edit box e Click the OK button to accept the new random seed An example dialog box for changing the random seed is shown below Random Seed Setting x M Using Default Random Seed Set Seed icoco omen Note Whether or not you use the default random seed depends on your needs Keeping the same seed will help you to duplicate your results However you can change the seed to generate a new series of random numbers such as to evaluate the stability of results for a given number of bootstrap simulations See chapter 4 of the Technical Documentation for an example 35 9 0 CHARACTERIZATION OF VARIABILITY FITTING DISTRIBUTIONS DATASET BY DATASET In this section we will describe how to characterize the variability in a dataset by fitting a single distribution to a dataset AuvTool can support your analysis of multiple datasets in this module However users must analyze datasets one by one and can choose a best fit to a dataset based on their own judgment AuvTool provides a feature to automatically help users to choose fits to their datasets for more details on this featu
93. s 56 ENTER OR LOAD DISTRIBUTIONS INFORMATION WITHOUT ORIGINATADA WA si sescsscisccassesssk soasssessssstcessantsiedstiesiteasitectescestous pateatacsssunsessiesede 57 11 1 Brief Explanation of Input Specification of Columns eeeeeeeeeeeeee 58 11 2 Input Distribution Information from the Keyboard cc ceeeseeeeeeeeeeee 59 11 3 Loading Existing Distribution Information from a File eee 60 114 Exiting the WO Gules 42 25 Riaesttacioces sft aaesace bes sadioanaseariae SAARE Measles 62 UNCERTAINTY ANALYSIS BOOTSTRAP SIMULATION scesseeeee 63 12 1 Doing a Bootstrap Simulation ce ceeceesceesceesseceteceeeceeeeeeeeessecnseeesees 65 12 2 Brief Explanation of the Graphical Displays ceceeeesceesseeeteeeteeeeees 66 12 3 Switching Between Graphs of Uncertainty and Probability Bands 67 il 13 0 14 0 15 0 16 0 17 0 18 0 19 0 12 4 Displaying and Saving the Bootstrap Simulation Data cesses 69 12 5 Entering the Module of Analyzing the Sampling Data of Statistics of Jnterest oien aac ee ieee ine Ma ad Se iat dn a eee eee 70 12 6 Exiting the Mod le 25 ac acacia e as n E Sanean ve tenaes A emis 71 ANALYZING THE SAMPLING DATA OF THE STATISTICS OF INTERESE aeaaeae aoaeiaa saasa aaa EEE ora Kai nas 72 13 1 Fitting a Distribution for a Statistic 0 cece eseeseeeecesecesecneeeeeeseeeeeeseenaes 76 13 2 Summarizing the Fitted Distributions for the Statistics of Interest 77
94. s and Y axis Select Blue in the Color labeled combo list box in the Grids group and Select the Inside Axes labeled radio box in the Tick Marks group If other options are unchanged when you click the Apply Now button or the Ok button The difference is that the Graph Control dialog box will not exit when you click the Apply Now button the graph will be automatically updated as follows Note 1 In the Axis page within Graph Control dialog box you may enter minimum and maximum values for the X Axis and the Y Axis For a cumulative 108 Fit a single distribution Input m Statistical Tests penio Fitting a Distribution for Dataset 1 n J Dataset 1 X 1 0 Distribution Type fos 41475914911794 Normal he Critical Value at 0 05 Estimation Method 0 8 Significant Level 2 o 258 Method Of Moment Max Likelihood Method E m PAA Not e o a a Data Passed 2 n 10 Go a4 m Anderson Darling Test E 7 Normal Value Outpat a 3 far 58062250395989 Mean 0 2 Critical Value at 0 05 Significant Level 0 827861 72 Standard Deviation 00 0 0 0 4 0 8 1 2 1 6 2 0 Passed or Not a 26 Passed Dataset 1 Fitting Result Summary Bootstrap Cancel distribution function it is recommended that you do not change the Y Axis minimum from zero or the Y Axis maximum from 1 For the X Axis you may type in the minimum and maxim
95. soosso 36 9 1 Selects Patasel es ceinen nE E E EE E e eats 39 9 2 Changing a Distribution Model for a Chosen Dataset ceeeeeeeseeeees 4 9 3 Changing Parameter Estimation Method cc eeeeseeceeeeceeeceeeeneeeeeeenees 4 9 4 Variability Analysis Results Summary for All Datasets eee 42 9 5 Entering Uncertainty Analysis Module cccccccesceeeceeeeeteeeeeenteeeees 42 9 60 Exiting the Mod le msi sac renni taie aaa EEA E AERA 43 CHARACTERIZATION OF VARIABILITY AND UNCERTAINTY BATCH ANALYSIS wo cscess sascssssvecscesssusciacouncseisvadsen cosbevstapens sin ucsuescasndesdocssvarsuapaeis 44 10 1 Showing a Graph of the Fitted Distribution for a Chosen Dataset 48 10 2 Visual Comparison of Fitted Distributions with a Chosen Dataset 49 10 3 Entering Uncertainty Analysis Module cceccceecceeeeeeeenseeeeeeteeeeees 51 10 4 Variability Analysis Result Summary for All Datasets eeeeeeeeeee 51 10 5 Uncertainty Analysis Result Summary for All Datasets 0 cesses 52 10 6 Saving the Current Batch Analysis Data and Property Sheet 0 52 10 7 Loading the Existing Batch Analysis Data and Property Sheet 53 10 8 Automatic Batch Analysis of the Sampling Distribution 0 0 08 53 Data for Statistics of Mites bea csc osec ch eats osodepaccehenasgeonsesacaaneade ds cicchacseeneess 53 10 9 Exiting the Batch Analysis Module cccecscccesecesecceseceeeeeeeecseeenteenee
96. t hand position of the Fit a Single Distribution window 40 e Click the dataset name you want to choose and e The graph will be updated automatically and the estimation results will also be updated 9 2 Changing a Distribution Model for a Chosen Dataset If you do not think that the current parametric probability distribution for the dataset you are analyzing is a good one you can change it To make a change of parametric distribution e Pull down the Distribution Type combo list box menu on the left side of the Fit a Single Distribution window e Click the distribution type you want to choose and e The graph will be updated automatically and the estimation results will also be updated 9 3 Changing Parameter Estimation Method AuvTool provides options for users to choose one of two parameter estimation methods The AuvTool sets MoMM as the default estimation method However users can freely choose either MoMM or MLE For more information on the two parameter estimation methods please see Parameter Estimation of Parametric Probability Distributions in the Technical Documentation To make a change of parameter estimation method e Click on the radio box of the method you want to choose e Click on the Go button on the left side of the Fit a Single Distribution window 41 e The graph will be updated automatically and the estimation results will also be updated Note For the uniform distribution MLE is not avail
97. the graph Note 2 Since there is no original data available in the second case shown on the previous page the program will only show the distribution that was specified by the user and cannot show any data If you want to edit save print the graph please see Working with a Graph on page 100 10 2 Visual Comparison of Fitted Distributions with a Chosen Dataset AuvTool implements a feature which allows users to visually compare different fitted distributions to a chosen dataset To invoke this feature e Click the Show All button on the row of the dataset you want to choose 49 e The program will display the graphs of different fits on the following Show All dialog box as illustrated on the next page Gamma Distribution Weibull Distribution Normal aaa Lognormal Distribution Distribution Show All Cumulative Probability Cumulative Probability Ey 08 8 E bad 0 6 4 Daa a a Cr 10 g f 0 4 A f Weibull S E E 0 2 5 5 0 0 0 0 First Parameter Second Parameter Distribution 2 oe Normal 0 827661 0 250126 0 091476 E 0 232851 0 295630 0 107962 g 9S 0 075590 0 096212 2 na 3 731945 0 087172 8 NA NA 0 2 gt O pa Show All Parameter Estimation Result Summary Table Beta Distribution Note 1 The Show All dialog box is not available for the cases which do not have origin
98. the uninstall feature of the Windows 98 Me Add Remove Software in the Control Panel Note Do not delete the files in the AuvTool directory Although you may disable the program it will not completely uninstall the program because there are files elsewhere on your system that should also be cleaned up To Run the Uninstall Program 1 Click the Start button 2 Choose Settings and then Control Panel 3 Double click Add Remove Programs in the Control Panel folder 4 Highlight AuvTool on the list of installed software 5 Click the Add Remove button Follow the instructions on the screen 3 0 GETTING STARTED 3 1 Starting AuvTool A program group called AuvTool is created when the software is installed AuvTool will be displayed in the Programs group in the Start Menu To start the AuvTool program click on the AuvTool program icon in the Start Menu The program will launch and a picture will be displayed The display is as follows The picture will disappear in 2 seconds after which the AuvTool mainframe window will appear and the program will be ready for use 3 2 Using AuvTool These are the steps or options involved in running AuvTool e Start AuvTool See Getting Started on page 8 e Data Entry Importing and Exporting see page 22 e Random Number Generators see page 30 e Random Seed Setting see page 34 ig AuvTool AuyToo1 lej x 9 Eie Edit View Uncertainty Bat
99. ther variables by selecting the desired variable or dataset listed in the combo box on the left top corner within the Bootstrap Simulation Graph tab page of the Bootstrap Simulation window 63 The dataset combo box to list the datasets needed to be analyzed The distribution type for the current dataset The parameter estimation method for the current dataset Graph title to the current dataset Legend for probability band Bootstrap Simulation Bootstrap Simulatior r Input Current Dataset Data Uncertainty Ranges Dataset 1 EE 95 Percent Current Distribution Type EE 90 Percent Weibull E 50 Percent Current Estimation Method r Graph of Moment Proffability Band C Ur brtainty of Statistics r Bootstrap Parameters No Of Replication B 500 Cumulative Probability No For Variabilit 500 Sample Size 10 Switch between the graphs of probability band and graph of uncertainty for specific statistics By default the program will display probability bands of the first dataset The number of data points for the current dataset Bootstrap parameter the number of bootstrap replications Pull down menu to change the statistic This will be visible if switched to the graph of uncertainty Bootstrap parameter the number of sampling variability
100. tion Dataset by Dataset module but also it provides the following capabilities of automatic batch analysis and visual comparison of different distribution types fitted to a dataset and uncertainty analysis for known distributions without the original datasets Users can finish their analyses of variability and uncertainty for multiple datasets without having to make any choices The program will automatically help users to choose best fits and to do uncertainty analysis For the criteria of selecting 45 a best fit to a dataset please refer to Criteria for Automatically Seeking a Best Distribution Model in the Batch Mode Analysis in the Technical Documentation The Batch Analysis module can support uncertainty analysis without original datasets if users can provide necessary distribution information Users cannot directly introduce the information into the batch analysis data and property sheet which must be done via the Link Distribution module For more details on how to introduce the known distribution information into the Batch Analysis module please see the module of Load Distributions Information on page 57 WARNING The user of AuvTool is cautioned that the availability of a batch mode technique for choosing a distribution based upon the K S test is not a substitute for the use of judgment The K S test is based upon a specific criterion which may or may not be important to a partic
101. tion method used in the case of parametric distributions and goodness of fit statistical test results in the case of parametric distributions To do this 51 e Click the Fitting Result Summary button on the left bottom corner of the Batch Fitting window e The program will display a popup Fitting Result Summary dialog box More information can be found on Variability Analysis Result Reporting on page 79 10 5 Uncertainty Analysis Result Summary for All Datasets After you have reviewed or modified the selection of parametric probability distributions and parameter estimation methods for all datasets you can obtain a summary of the uncertainty in the mean and standard deviation for all datasets To do this e Click the Uncertainty Result Summary button on the left bottom corner of Batch Fitting window e The program will display a popup Uncertainty Analysis Summary dialog box More information can be found on Uncertainty Analysis Result Reporting on page 84 10 6 Saving the Current Batch Analysis Data and Property Sheet You can save for future analysis your choices made on the datasets by saving the current Batch Analysis Data and Property Sheet to an AuvTool file format To save the current data sheet e Click the Save button on the left bottom comer of Batch Fitting window e The program will display a Save as file dialog box 52 e Enter a filename with an extension of ss3 Click the Save butto
102. tomatically and the estimation results and goodness of fit test results will also be updated 13 2 Summarizing the Fitted Distributions for the Statistics of Interest AuvTool provide a module to summarize the distributions fitted to the sampling distribution data for the statistics of interest You can enter into the module by clicking on the Uncertainty Distribution Summary button on the right bottom corner of the Fitting Uncertainty Sampling Distribution page The program will display the Summary on the Fitted Distributions to the Statistics of Interest dialog box More information on the summary can be found in Uncertainty Analysis Result Reporting on page 84 13 3 Exiting the Module You have three ways to exit the Analyzing the Sampling Data of the Statistics of Interest module TT If you just want to switch to the other pages within the Bootstrap Simulation window click one of them on the page tabs If you have completed all analyses and also want to exit the uncertainty analysis module e Click the OK button on the Bootstrap Simulation window e Click the Cancel button on the Bootstrap Simulation window 78 14 0 VARIABILITY ANALYSIS RESULT REPORTING The purpose of the Variability Analysis Result Reporting module is to summarize the selected results of variability analysis for the user You can enter the module either by clicking on the Fitting Distribution Summary butto
103. ular analyst or decision maker in the context of a specific problem The K S test does not screen for results that may be physically implausible such as a probability of sampling negative values for a quantity that must be non negative The appropriateness of selection of a distribution depends on the data quality objective of each analysis which may differ from one situation to another Therefore uncritical application of the batch mode feature of AuvTool for seeking a best fit distribution is likely to lead to inappropriate selection of a probability distribution model in some cases It is the user s responsibility to evaluate the automatically selected parametric probability distribution for appropriateness with respect to the user s own criteria and needs 46 Note 1 All notes in the Fitting Distribution Dataset by Dataset module on page 41 also apply to the Batch Analysis module except the Note 1 Note 2 In the batch analysis sheet each row represents a dataset All choices and actions made on the selected row will be effective only for the dataset on the row Note 3 In the column of Distribution Choice Auto is not a distribution type but an option The program sets the Auto as the default option Auto means that users let the program automatically choose a good fit for the selected dataset For those cases that do not have original data there is no Auto option available and users cannot m
104. um values that you prefer Note 2 If you wish to abandon your entries click the Cancel button The Graph Control dialog box will disappear and no change will be made to the graph 17 2 2 Editing Titles By using the Title feature you can enter or modify the graph title the bottom title and the left and right titles You can also adjust the display direction of the left and right titles To invoke the feature first bring up the Graph Control dialog box as introduced in the first section of this chapter and then click on the Titles tab in the Graph Control dialog box to enable the Titles page which is shown on the next page Introduction to the Controls within Titles Page 109 Graph Title labeled edit box In this box you can enter or modify text for the graph title which can be up to 80 characters in length This title appears centered at the top of the graphing window Graph Control x Titles Axis Fonts Design Sasseseeessssnesensd Graph Title Fitting a Distribution for Dataset 1 Bottom Title Dataset Left Title Title Cumulative Probability Horizontal Up C Down Right Title Title C Up Horizontal Cancel Apply Now Help The Titles page within the Graph Control box Bottom Title labeled edit box In this box you can enter or modify text for the bottom title which can be up to 80 characters in length This title ap
105. uts for one variable press the lt Enter gt key to move to the next row to input the distribution information for other variables Repeating this process until you finish inputs for all variables If you want to change the data in a cell just move the cursor to the cell type another value and press lt Enter gt 11 3 Loading Existing Distribution Information from a File You can load the existing distribution information files into the Link Distribution sheet In this module AuvTool support three file formats AuvTool file format Microsoft Excel 97 file format and tab delimited text file To load a file e Click the Link Distribution Information button of the left bottom corner of the Link the distribution information of variables without the original data dialog box e The program will display the following Choose File Format dialog box Choose File Format x AuvTool File Format Microsoft Excel 97 File Format C Tab Delimited Text File Format e Select the format of the file you want to open then Click the OK button e The program will display a standard Open File Dialog as shown in the Data Entry Importing and Exporting module on the page 22 60 e Enter the file name and click the Open button The program will load the existing distribution files into the Link Distribution sheet An example Link Distribution sheet is shown on the next page after loading the existing distribution file Note 1 In th
106. vTool does not require that the names representing different datasets in the same sheet be unique However for your convenience in identifying different datasets we recommend that you use different names for different data sets Note 3 When the program imports data from other application programs such as from the Excel sometimes the name or titles of datasets are located in the first row In this situation The first row is title row labeled check box must be enabled by clicking on it This check box is located immediately to the right of the text box for Name Dataset entry If there are no names or titles for the imported datasets users have to name them as introduced above Note 4 For any AuvTool sheet files all of the names of all datasets within the same file are located at either the column header or the first row 6 7 Data Input Checking AuvTool has a feature to logically check the users data input AuvTool assumes that the data within any cells are valid numerical values except for the first row when the The first row is title row labeled check box is enabled The feature will be invoked when users try to make further analysis If there exists any invalid non numerical values such as a text string in a particular cell the program will pop up a message box showing not a valid numerical value at row n column m Users must correct all the exceptions before they can do further data analysis 29 7 0 RANDOM NUMBER GENE
107. value x in the dataset x Efron 1979 The CDF for this function is therefore a step function of original data set x where each value x is assigned a cumulative probability of i n for i 1 2 n An example of an empirical distribution represented a step function for a data set with n 10 is provided in Figure 5 1 0 8 0 6 0 4 0 2 Cumulative Probability 0 2 4 6 8 Example Data Figure 5 1 An example of an Empirical Distribution Represented a Step Function 19 Table 5 2 Conventions for 1 Parameter and 2 Parameter Terms Used in AuvTool 1a om Name 1 Parameter 2 Parameter Normal Mean u Standard Deviation o Lognormal Mean of ln x Unx Standard Deviation of In x Oinx Beta Shape a Shape B Gamma Scale a Shape B Weibull Scale k Shape c Uniform Minimum a Maximum b Symmetric Triangle a b Please refer to the Technical Documentation for detailed definitions of these distributions and other relevant information 5 3 AuvTool Conventions 1 parameter and 2 parameter Each parametric distribution contained in this version of AuvTool is described by two parameters In some modules we use the 7 parameter and 2 parameter to represent the two parameters The specific interpretation of each parameter differs for different types of parametric distributions is presented in Table 5 2 Note The user does not have to be familiar with the mathematical formulation
108. ve the Graph Control underline the text Size Group Smart Scale labeled check box default is on Check this box to have the Graph Control automatically use smaller type if the size you specify using the Smaller Bigger scroll bar makes the text too large for the available space If the Graph Control cannot make the type small enough to fit the text will not display at all If you do not check Smart Scale the Graph Control will not attempt to use 114 type smaller than you specify with the Smaller Bigger scroll bar If the text is too large for the space available it simply will not display Smaller Bigger labeled scroll bar This scroll bar lets you set the size of type If Smart Scale is selected the Graph Control may override your setting to make the text small enough to fit in the graphing window Each click on the Smaller end of the scroll bar decreases the text size by 5 arbitrary units to a minimum of 50 and each click on the Bigger end increases it by 5 units to a maximum of 500 The initial size depends on which type of text you are sizing Reset labeled button Click this button to reset the text size to the default Editing the Fonts of a Graph According to the introductions above you can edit the font setting for graph titles and other objects To do this e Select the radio box in the Apply to group you want to modify its font setting e Select the font name check font styles adjust font size if desired
109. viation and the parameters of the fitted distribution You might want to fit parametric distributions to the sampling distribution data for the statistics of interest AuvTool offers a feature to do this To enter the module of Analyzing the Sampling Data of Statistics of Interest click on the Fitting Uncertainty Sampling Distribution tab page within the Bootstrap Simulation window For more information on the module please see the section on Analyzing the Sampling Data of the Statistics of Interest on page 72 70 Note If you tried to enter the module without having finished a bootstrap simulation for some datasets or variables the program will provide a warning message box to show you the datasets or variables for which bootstrap simulation has not been completed You can go ahead to do the analysis of fitting distributions to the sampling data for those datasets for which bootstrap simulations have been done However you cannot do such an analysis for the datasets for which bootstrap simulations have not been done You can go back to the Bootstrap Simulation Graph page to do the bootstrap simulation for such datasets 12 6 Exiting the Module You have two ways to exit the Uncertainty Analysis Bootstrap Simulation module e Click the OK button on the Bootstrap Simulation window e Click the Cancel button on the Bootstrap Simulation window 71 13 0 ANALYZING THE SAMPLING DATA OF THE STA

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