Version 4.0: Origin User's Manual
Contents
1. Ae Ag Brief Description Exponential decay 3 Sample Curve Parameters Number 7 Names y0 Al tl A2 t2 A3 t3 Meanings y0 offset Al amplitude t1 decay constant A2 amplitude t2 decay constant A3 amplitude t3 decay constant Initial Values yO 0 0 vary Al 1 0 vary t1 1 0 vary A2 1 0 vary t2 1 0 vary A3 1 0 vary t3 1 0 vary Lower Bounds none Upper Bounds none Script Access expdec3 x y0 A1 t1 A2 t2 A3 t3 Function File FITFUNC EXPDEC3 FDF Last Updated 11 14 00 Page 52 of 166 ExpDecay1 Function ya ys Agro Brief Description Exponential decay 1 with offset Sample Curve y A ft offset y 1 center x 1 amplitude 10 decay constantt 1 Parameters Number 4 Names y0 x0 Al t1 Meanings y0 offset xO center Al amplitude t1 decay constant Initial Values yO 0 0 vary x0 0 0 vary Al 10 vary t1 1 0 vary Lower Bounds none Upper Bounds none Script Access expdecay1 x y0 x0 A 1 t1 Function File FITFUNC EXPDECY 1 FDF Last Updated 11 14 00 Page 53 of 166 ExpDecay2 Function y 2yg ES Ae o Ae 07 Brief Description Exponential decay 2 with offset Sample Curve center x 0 offset y 0 y A trA t o amplitude A 1 decay congant t 1 Oa Xy 9 amplitude A 2 decay constant t 2 Yo Parameters Number 6 Names y0 x0 Al t1 A2 t2 Meanings y0 o2. Parameters Number 4 Names y0 xc w A Meanings y0 offset xc center w width A amplitude Initial Values yO 0 0 vary xc 1 0 vary w 1 0 vary A 1 0 vary Lower Bounds w gt 0 0 Upper Bounds none Script Access extreme Xx y0 xc w A Function File FITFUNC EXTREME FDF Last Updated 11 14 00 Page 98 of 166 Gauss Function A ME y 2 Y t me wNTI 2 Brief Description Area version of Gaussian function Sample Curve xc yc amp 0 offset yO 1 center xc 2 width w 1 5 area A 5 yczyO Aj w sqit pi 23 wewl fsqrt in 4 Parameters Number 4 Names y0 xc w A Meanings y0 offset xc center w width A area Initial Values yO 0 0 vary xc 0 0 vary w 1 0 vary A 10 vary Lower Bounds w gt 0 0 Upper Bounds none Script Access gauss x y0 xc w A Function File FITFUNC GAUSS FDF Last Updated 11 14 00 Page 99 of 166 GaussAmp Function 2 x x y 2w y y Ae Brief Description Amplitude version of Gaussian peak function Sample Curve 2w wiisqrt In 4 xe yOrA Faw gt O offset yO 0 center xc 0 width w 1 amplitude A 10 Parameters Number 4 Names y0 xc w A Meanings y0 offset xc center w width A area Initial Values yO 0 0 vary xc 0 0 vary w 1 0 vary A 10 vary Lower Bounds w gt 0 0 Upper Bounds none Script Access gaussamp x
3. Sample Curve 2 a 1 x 1 powerbe2 power b 1 yab y cab 0 3 0 a Parameters Number 2 Names a b Meanings a coefficient b power Initial Values a 1 0 vary b 1 0 vary Lower Bounds none Upper Bounds none Script Access pow2p2 x a b Function File FITFUNC POW2P2 FDF Last Updated 11 14 00 Page 134 of 166 Pow2P3 Function 1 Eje gt 1 ax Brief Description Two parameter power function Sample Curve 0 0 wy asp a 1 power b 2 Parameters Number 2 Names a b Meanings a coefficient b power Initial Values a 1 0 vary b 1 0 vary Lower Bounds none Upper Bounds none Script Access pow2p3 x a b Function File FITFUNC POW 2P3 FDF Last Updated 11 14 00 Page 135 of 166 Power Function A y x Brief Description One parameter power function Sample Curve x 0 a 5 as power A Ds yaa ho asp Parameters Number 1 Names A Meanings A power Initial Values A 1 0 vary Lower Bounds none Upper Bounds none Script Access power x A Function File FITFUNC POWER FDF Last Updated 11 14 00 Page 136 of 166 PowerO Function P y y Alx x Brief Description Symmetric power function with offset Sample Curve Pap g i y A xol yO A Parameters Number 4 Names y0 xc A P Meanings y0 offset xc center A amplitude P power Initial Values yO
4. Sample Curve y A ft offset y 1 center x 1 amplitude 10 decay constantt 1 Parameters Number 4 Names y0 x0 Al t1 Meanings y0 offset xO center Al amplitude t1 decay constant Initial Values yO 0 0 vary x0 0 0 vary Al 10 vary t1 1 0 vary Lower Bounds none Upper Bounds none Script Access expdecay1 x y0 x0 A 1 t1 Function File FITFUNC EXPDECY 1 FDF Last Updated 11 14 00 Page 8 of 166 ExpDecay2 Function y 2yg ES Ae o Ae 07 Brief Description Exponential decay 2 with offset Sample Curve center x 0 offset y 0 y A trA t amplitudeA 1 decay congant t 1 Oh rt amplitude A 2 decay constant t 2 Yo Parameters Number 6 Names y0 x0 Al t1 A2 t2 Meanings y0 offset x0 center Al amplitude t1 decay constant A2 amplitude t2 decay constant Initial Values yO 0 0 vary x0 0 0 vary Al 10 vary t1 1 0 vary A2 10 vary t2 1 0 vary Lower Bounds none Upper Bounds none Script Access expdecay2 x y0 x0 A1 t1 A2 t2 Function File FITFUNC EXPDECY2 FDF Last Updated 11 14 00 Page 9 of 166 ExpDecay3 Function y Yo Ae o 4 Ae 07 Aye Ct Brief Description Exponential decay 3 with offset Sample Curve 0 y 0 A1 A 2 3 center x0 2 A1210 A 2210 A3 5 t121 122213 3 Y A1 t1 A2 t2 A3 t3 Parameters Number 8 Names y0 x0 Al tl A2 t2 A3 t3 Meanings y0
5. 141 142 143 144 145 146 147 148 149 150 151 152 153 154 Last Updated 11 14 00 Page 140 of 166 BET Function y abx 12 b 2 x p 1 Brief Description BET model Sample Curve Parameters Number 2 Names a b Meanings a coefficient b coefficient Initial Values a 1 0 vary b 5 0 vary Lower Bounds none Upper Bounds none Script Access bet x a b Function File FITFUNC BET FDF Last Updated 11 14 00 Page 141 of 166 BETMod Function X d a 4 bx a b x Brief Description Modified BET model Sample Curve az1 b 5 x al a b Parameters Number 2 Names a b Meanings a coefficient b coefficient Initial Values a 1 0 vary b 5 0 vary Lower Bounds none Upper Bounds none Script Access betmod x a b Function File FITFUNC BETMOD FDF Last Updated 11 14 00 Page 142 of 166 Holliday Function y a bx exl Brief Description Holliday model a Yield density model for use in agriculture Sample Curve x b sq rib 4ac y2c b 2 c AcK Aac b x b 2c a 1 b 2 1 y 0 0 yu T xe bes qrib 4ac 2c Parameters Number 3 Names a b c Meanings a coefficient b coefficient c coefficient Initial Values a 1 0 vary b 1 0 vary c 1 0 vary Lower Bounds none Upper Bounds none Script Access holliday x a b c Function File FITFUNC HOLLIDAY FDF Last Updated 11 14 00 Page 1
6. D A1 Parameters Number 4 Names Al A2 x0 p Meanings A1 initial value A2 final value x0 center p power Initial Values A1 0 0 vary A2 1 0 vary x0 1 0 vary p 1 5 vary Lower Bounds p 0 0 Upper Bounds none Script Access logistic x A1 A2 x0 p Function File FITFUNC LOGISTIC FDF Last Updated 11 14 00 Page 72 of 166 SGompertz Function y ag C6 Brief Description Gompertz growth model for population studies animal growth Reference Seber G A F Wild C J 1989 Nonlinear Regression John Wiley amp Sons Inc pp 330 331 Sample Curve y a kie amplitude a 1 center xc 1 k 1 Parameters Number 3 Names a xc k Meanings a amplitude xc center k coefficient Initial Values a 1 0 vary xc 1 0 vary k 1 0 vary Lower Bounds a gt 0 0 k gt 0 0 Upper Bounds none Script Access sgompertz x a xc k Function File FITFUNC GOMPERTZ FDF Last Updated 11 14 00 Page 73 of 166 SLogistic1 Function E a y k x x l e Brief Description Sigmoidal logistic function type 1 Reference Seber G A F Wild C J 1989 Nonlinear Regression John Wiley amp Sons Inc pp 328 330 Sample Curve y 0 Parameters Number 3 Names a xc k Meanings a amplitude xc center k coefficient Initial Values a 1 0 vary xc 1 0 vary k 1 0 vary Lower Bounds xc gt 0 Upper Bounds none Scr
7. Function File FITFUNC BELEHRAD FDF Last Updated 11 14 00 Page 124 of 166 BINeld Function y a bx J Brief Description Bleasdale Nelder model Sample Curve e 1 b xe a c 0 5 f 1 a 1b S gt pfi tc ae b 1 a b 3 y0 UL prifca 0 0 Parameters Number 4 Names a b c f Meanings a coefficient b coefficient c coefficient f power Initial Values a 1 0 vary b 1 0 vary c 0 5 f 1 0 Lower Bounds none Upper Bounds none Script Access bineld x a b c f Function File FITFUNC BLNELD FDF Last Updated 11 14 00 Page 125 of 166 BINeldSmp Function y a bx Brief Description Simplified Bleasdale Nelder model Sample Curve Parameters Number 3 Names a b c Meanings a coefficient b coefficient c coefficient Initial Values a 1 0 vary b 1 0 vary c 2 0 5 Lower Bounds none Upper Bounds none Script Access blneidsmp x a b c Function File FITFUNC BLNELDSP FDF Last Updated 11 14 00 Page 126 of 166 FreundlichEXT Function Brief Description Extended Freundlich model Sample Curve e e de f c e y 0 b gt 0 y a y a1 b 5 Ve b c e parer c05 e g e Parameters Number 3 Names a b c Meanings a coefficient b coefficient c power Initial Values a 1 0 vary b 1 0 vary c 0 5 Lower Bounds none Upper Bounds none Script Access freundlichext x
8. Exp3P1Md Function b a y e xte Brief Description Three parameter exponential function Reference Ratkowksy David A 1990 Handbook of Nonlinear Regression Models Marcel Dekker Inc 4 3 34 Sample Curve Parameters Number 3 Names a b c Meanings a coefficient b coefficient c coefficient Initial Values a 1 0 vary b 1 0 vary c 0 5 Lower Bounds none Upper Bounds none Script Access exp3p1md x a b c Function File FITFUNC EXP3P1MD FDF Last Updated 11 14 00 Page 47 of 166 Exp3P2 Function 2 a bx cx e Brief Description Three parameter exponential function Reference Ratkowksy David A 1990 Handbook of Nonlinear Regression Models Marcel Dekker Inc 4 3 39 Sample Curve X hi2c 1 y h e E 0 5 c 0 5 0 8 0 25 1 y pre 0 e Xr hi2c eg Parameters Number 3 Names a b c Meanings a coefficient b coefficient c coefficient Initial Values a 1 0 vary b 1 0 vary c 0 5 Lower Bounds none Upper Bounds none Script Access exp3p2 x a b c Function File FITFUNC EXP3P2 FDF Last Updated 11 14 00 Page 48 of 166 ExpAssoc Function y y tA 1 e A 1 ag Brief Description Exponential associate Sample Curve y yO AI A2 offs ety 1 amplitud e A 1 width t7 1 amplitud e A 2 Parameters Number 5 Names y0 Al tl A2 t2 Meanings y0 offset Al amplitude t1
9. b cx 1 ax Brief Description Rational function type 0 Reference Ratkowksy David A 1990 Handbook of Nonlinear Regression Models Marcel Dekker Inc 4 3 24 Sample Curve Parameters Number 3 Names a b c Meanings a coefficient b coefficient c coefficient Initial Values a 1 0 vary b 1 0 vary c 0 5 Lower Bounds none Upper Bounds none Script Access rational0 x a b c Function File FITFUNC RATIONO FDF Last Updated 11 14 00 Page 20 of 166 Sine Function y Ass rd w Brief Description Sine function Sample Curve C enter xc 0 Widthw 1 IA Amplitude Az 1 xc 0 Parameters Number 3 Names xc w A Meanings xc center w width A amplitude Initial Values xc 0 0 vary w 1 0 vary A 1 0 vary Lower Bounds w gt 0 0 Upper Bounds none Script Access sine x xc w A Function File FITFUNC SINE FDF Last Updated 11 14 00 Page 21 of 166 Voigt Function 21n2 w e ges use s E 2 dt Ww X X 7 qi a aad Pes Wg Wg Brief Description Voigt peak function Sample Curve Al offset yYO 0 center xc 5 amplitud e A 1 wG 1 wL 1 Parameters Number 5 Names y0 xc A wG wL Meanings y0 offset xc center A amplitude wG Gaussian width wL Lorentzian width Initial Values yO 0 0 vary xc 0 0 vary A 1 0 vary wG 1 0 vary wL 1 0 vary Lower Bounds wG gt 0 0 wL gt 0 0
10. 1 0 vary Lower Bounds none Upper Bounds none Script Access expgro1 x y0 A 1 t1 Function File FITFUNC EXPGRO1 FDF Last Updated 11 14 00 Page 56 of 166 ExpGro2 Function XI ty y y t Aen Ae Brief Description Exponential growth 2 Sample Curve offset yO 0 amplitude Ay 1 y A1 t1 442 02 growth constant t 1 1 amplitude A2 2 growth constant 2 2 0 yo A44 42 Parameters Number 5 Names y0 Al tl A2 t2 Meanings y0 offset Al amplitude t1 growth constant A2 amplitude t2 growth constant Initial Values yO 0 0 vary Al 1 0 vary t1 1 0 vary A2 1 0 vary t2 1 0 vary Lower Bounds none Upper Bounds none Script Access expgro2 x y0 A1 t1 A2 t2 Function File FITFUNC EXPGRO2 FDF Last Updated 11 14 00 Page 57 of 166 ExpGro3 Function y yt Ae Ae 4 Ae Brief Description Exponential growth 3 Sample Curve y 1 2 A417 4 A27 t2 A3 t3 offset yg 0 am plitude A121 ty t2 t3 1 2 3 am plitude 42 2 am plitude 43 3 0 yOrA1 42 A43 Parameters Number 7 Names y0 Al tl A2 t2 A3 t3 Meanings y0 offset Al amplitude tl growth constant A2 amplitude t2 growth constant A3 amplitude t3 growth constant Initial Values yO 0 0 vary Al 1 0 vary tl 1 0 vary A2 1 0 vary t2 1 0 vary A3 1 0 vary t3 1 0 vary Lower Bounds none Upper Bounds none Scrip
11. 1 0 vary c 0 5 Lower Bounds none Upper Bounds none Script Access rational3 x a b c Function File FITFUNC RATION3 FDF Last Updated 11 14 00 Page 149 of 166 Rational4 Function y c x a Brief Description Rational function type 4 Sample Curve Parameters Number 3 Names a b c Meanings a coefficient b coefficient c coefficient Initial Values a 1 0 vary b 1 0 vary c 0 5 Lower Bounds none Upper Bounds none Script Access rational4 x a b c Function File FITFUNC RATION4 FDF Last Updated 11 14 00 Page 150 of 166 Reciprocal Function a3 1 i a t bx Brief Description Two parameter linear reciprocal function Sample Curve a 1 b 1 Parameters Number 2 Names a b Meanings a coefficient b coefficient Initial Values a 1 0 vary b 1 0 vary Lower Bounds none Upper Bounds none Script Access reciprocal x a b Function File FITFUNC RECIPROC FDF Last Updated 11 14 00 Page 151 of 166 ReciprocalO Function HE 1 Ax y Brief Description One parameter linear reciprocal function Sample Curve xe A Parameters Number 1 Names A Meanings A coefficient Initial Values A 1 0 vary Lower Bounds none Upper Bounds none Script Access reciprocalO x A Function File FITFUNC RECIPRO FDF Last Updated 11 14 00 Page 152 of 166 Reciprocal1t Function 53 1 x A Brief Des
12. Function File FITFUNC IN VSPOLY FDF Last Updated 11 14 00 Page 104 of 166 LogNormal Function In xix F y Yo e 2w 27 wx Brief Description Log Normal function Sample Curve xc yO 4 Aw offset yO 0 center xc 150 width we0 3 arrplitude A 1 y0 Parameters Number 4 Names y0 xc w A Meanings y0 offset xc center w width A amplitude Initial Values y0 0 0 vary xc 1 0 vary w 1 0 vary A 1 0 vary Lower Bounds xc gt 0 w gt 0 Upper Bounds none Script Access lognormal x y0 xc w A Function File FITFUNC LOGNORM FDF Last Updated 11 14 00 Page 105 of 166 Logistpk Function LX 7Xc 4Ae y yer _ X xe lee Brief Description Logistic peak function Sample Curve 20 we offset y 0 0 center xc 1 widthwel xc ye 0 amplitude 0 1 Parameters Number 4 Names y0 xc w A Meanings y0 offset xc center w width A amplitude Initial Values yO 0 0 vary xc 1 0 vary w 1 0 vary A 1 0 vary Lower Bounds w gt 0 0 Upper Bounds none Script Access logistpk x y0 xc w A Function File FITFUNC LOGISTPK Last Updated 11 14 00 Page 106 of 166 Lorentz Function 2A w Y Yo T A x x w Brief Description Lorentzian peak function Sample Curve xc yc yS OHA w pi Parameters Number 4 Names y0 xc w A Meanings y0 offset xc center w widt
13. Script Access response2 x Amin Amax1 Amax2 x0 1 x0 2 h1 h2 Function File FITFUNC BIPHASIC FDF Last Updated 11 14 00 Page 114 of 166 DoseResp Function A A A YS ae log xp x p 1 10 Brief Description Dose response curve with variable Hill slope given by parameter p Sample Curve AlsA2 p 0 yaA2 batten asymptote prin 10 2 A1 A121 top asymptate login amp 1 A2y2 A2 2 certet Log 1 A hill Sope p 0 2 Parameters Number 4 Names Al A2 LOGx0 p Meanings Al bottom asymptote A2 top asymptote LOGxO center p hill slope Initial Values Al 1 0 vary A2 100 0 vary LOGxO 5 0 vary p 1 0 vary Lower Bounds none Upper Bounds none Script Access response1 x A7 A2 LOGXx0 p Function File FITFUNC DRESP FDF Last Updated 11 14 00 Page 115 of 166 OneSiteBind Function B x max Kli x Brief Description One site direct binding Rectangular hyperbola connects to isotherm or saturation curve Sample Curve Bmax gt 0 ki gt 0 Bmax t tote op asymptote y Bmax kt Bmax 1 median k1 2 x k1 Parameters Number 2 Names Bmax K1 Meanings Bmax top asymptote K1 median Initial Values Bmax 1 0 vary K1 1 0 vary Lower Bounds none Upper Bounds none Script Access binding1 x Bmax K1 Function File FITFUNC BIND1 FDF Last Updated 11 14 00 Page 116 of 166 OneSiteComp
14. Upper Bounds none Script Access voigt5 x y0 xc A wG wL Function File FITFUNC VOIGTS FDF Last Updated 11 14 00 Page 22 of 166 2 Chromatography Functions CCE ECS Gauss GaussMod GCAS Giddings 24 25 26 27 28 29 Last Updated 11 14 00 Page 23 of 166 CCE Function exe y y y tAle 2 B 1 0 5 1 tanh k x x J e 55 709 Brief Description Chesler Cram peak function for use in chromatography Sample Curve offs et y 0 Keg Xag 12 3 A 1 Parameters Number 9 Names y0 xcl A w k2 xc2 B k3 xc3 Meanings y0 offset xcl unknown A unknown w unknown k2 unknown xc2 unknown B unknown k3 unknown xc3 unknown Initial Values yO 0 0 vary xcl 1 0 vary A 1 0 vary w 1 0 vary k2 1 0 vary xc2 1 0 vary B 1 0 vary k3 1 0 vary xc3 1 0 vary Lower Bounds w gt 0 0 Upper Bounds none Script Access cce x y0 xc1 A w k2 xc2 B k3 xc3 Function File FITFUNC CHESLECR FDF Last Updated 11 14 00 Page 24 of 166 ECS Function where z Brief Description Edgeworth Cramer peak function for use in chromatography Sample Curve Parameters Number 6 Names yO xc A w a3 a4 12 2 2 2 ient 62 3 3 10a offset y 1 center x 0 am plitude 4 5 width w 1 ar2 a2 2 15z e 452 15 Meanings y0 offset xc center A amplitude w width a3 unknown a4 unknown I
15. t0 gt 0 0 Upper Bounds none Script Access gaussmod x y0 A xc w t0 Function File FITFUNC GAUSSMOD FDF Last Updated 11 14 00 Page 27 of 166 GCAS Function A i 212 4 a fi go quy ua wv 270 2 i pcs z Ww H 2 3z H z 62 3 Brief Description Gram Charlier peak function for use in chromatography Sample Curve offset yo 1 center xc 0 area A 1 width w 1 a3 0 01 a4 0 001 Parameters Number 6 Names yO xc A w a3 a4 Meanings y0 offset xc center A amplitude w width a3 unknown a4 unknown Initial Values yO 0 0 vary xc 0 0 vary A 1 0 vary w 1 0 vary a3 0 01 vary a4 0 001 vary Lower Bounds w 0 0 Upper Bounds none Script Access gcas x y0 xc A w a3 a4 Function File FITFUNC GRMCHARL FDF Last Updated 11 14 00 Page 28 of 166 Giddings Function A x 2r yer L li Ww X Ww Brief Description Giddings peak function for use in chromatography Sample Curve offset y 1 center 5 width we1 area A Parameters Number 4 Names y0 xc w A Meanings y0 offset xc center w width A area Initial Values yO 0 0 vary xc 1 0 vary w 1 0 vary A 1 0 vary Lower Bounds w gt 0 0 Upper Bounds none Script Access giddings x yO xc w A Function File FITFUNC GIDDINGS FDF Last Updated 11 14 00 Page 29 of 166 3 Exponential Functio
16. y la QU g I y la ge p a 31 Brief Description Sigmoidal Richards function type 1 Reference Seber G A F Wild C J 1989 Nonlinear Regression John Wiley amp Sons Inc pp 332 337 Sample Curve y a y 2 20 x1 y1 yz0 y4z 1ik ln 1 d a 1 d xc Parameters Number 4 Names a xc d k Meanings a unknown xc center d unknown k coefficient Initial Values a 1 0 vary xc 1 0 vary d 5 vary k 0 5 vary Lower Bounds a gt 0 0 k gt 0 0 Upper Bounds none Script Access srichards1 x a xc d k Function File FITFUNCNSRICHARI FDF Last Updated 11 14 00 Page 77 of 166 SRichards2 Function y all d pe t6 PT Brief Description Sigmoidal Richards function type 2 Reference Seber G A F Wild C J 1989 Nonlinear Regression John Wiley amp Sons Inc pp 332 337 Sample Curve d gt 1 a k gt O a 1 y a center xc 1 d 3 k 0 2 Parameters Number 4 Names a xc d k Meanings a unknown xc center d unknown k coefficient Initial Values a 1 0 vary xc 1 0 vary d 5 0 vary k 1 0 vary Lower Bounds a 0 0 k 0 0 Upper Bounds none Script Access srichards2 x a xc d k Function File FITFUNC SRICHAR2 FDF Last Updated 11 14 00 Page 78 of 166 SWeibull1 Function y Al e C Di Brief Description Sigmoidal Weibull function type 1 Reference Seber G A F
17. 0 vary A2 1 0 vary t2 1 0 vary Lower Bounds t1 0 0 t2 0 0 Upper Bounds none Script Access expgrow2 x y0 x0 A1 11 A2 12 Function File FITFUNC EXPGROW2 FDF Last Updated 11 14 00 Page 12 of 166 Gauss Function A ME y 2 Y t me wNTI 2 Brief Description Area version of Gaussian function Sample Curve xc yc amp 0 offset yO 1 center xc 2 width w 1 5 area A 5 yczyO Aj w sqit pi 23 wewl fsqrt in 4 Parameters Number 4 Names y0 xc w A Meanings y0 offset xc center w width A area Initial Values yO 0 0 vary xc 0 0 vary w 1 0 vary A 10 vary Lower Bounds w gt 0 0 Upper Bounds none Script Access gauss x y0 xc w A Function File FITFUNC GAUSS FDF Last Updated 11 14 00 Page 13 of 166 GaussAmp Function 2 x x y 2w y y Ae Brief Description Amplitude version of Gaussian peak function Sample Curve 2w wiisqrt In 4 xe yOrA Faw gt O offset yO 0 center xc 0 width w 1 amplitude A 10 Parameters Number 4 Names y0 xc w A Meanings y0 offset xc center w width A area Initial Values yO 0 0 vary xc 0 0 vary w 1 0 vary A 10 vary Lower Bounds w gt 0 0 Upper Bounds none Script Access gaussamp x yO xc w A Function File FITFUNC GAUSSAMP FDF Last Updated 11 14 00 Page 14 of 166 Hyperbl Function __ Fix P
18. 0 0 vary xc 5 0 vary A 1 0 vary P 0 5 vary Lower Bounds A gt 0 0 Upper Bounds none Script Access power0 x y0 xc A P Function File FITFUNC POWERO FDF Last Updated 11 14 00 Page 137 of 166 Power1 Function p y Alx X Brief Description Symmetric power function Sample Curve Parameters Number 3 Names xc A P Meanings xc center A amplitude P power Initial Values xc 0 0 vary A 1 0 vary P 2 0 vary Lower Bounds A gt 0 0 P gt 0 0 Upper Bounds none Script Access power1 x xc A P Function File FITFUNC POWER1 FDF Last Updated 11 14 00 Page 138 of 166 Power2 Function y Ax x x lt X y Alx x n x gt X Brief Description Asymmetric power function Sample Curve y 1 Ap y 1 2A pu center xc 0 amplitude A 1 power pl 2 power pu 1 5 xo 1 A xc 1 A Parameters Number 4 Names xc A pl pu Meanings xc center A amplitude pl power pu power Initial Values xc 0 0 vary A 1 0 vary p1 2 0 vary pu 2 0 vary Lower Bounds A gt 0 0 p1 gt 0 0 pu gt 0 0 Upper Bounds none Script Access power2 x xc A pl pu Function File FITFUNC POWER2 FDF Last Updated 11 14 00 Page 139 of 166 10 Rational Functions BET BETMod Holliday Hollidayl Nelder RationalO Rationall Rational2 Rational3 Rational4 Reciprocal Reciprocal0 Reciprocall ReciprocalMod
19. A2 1 0 vary x0 0 0 vary dx 1 0 vary Lower Bounds none Upper Bounds none Constraints dx 0 Script Access boltzman x A1 A2 x0 dx Function File FITFUNC BOLTZMAN FDF Last Updated 11 14 00 Page 5 of 166 Dhyperbl Function __ Bx Ex Ptx P x y Px Brief Description Double rectangular hyperbola function Sample Curve PIRA ng p4 2 p6 5 xp x p4 x p2 0 0 Pppp Yp papi 5 Parameters Number 5 Names P1 P2 P3 P4 P5 Meanings Unknowns 1 5 Initial Values P1 1 0 vary P2 1 0 vary P3 1 0 vary P4 1 0 vary P5 1 0 vary Lower Bounds none Upper Bounds none Script Access dhyperbl x P1 P2 P3 P4 P5 Function File FITFUNC DHYPERBL FDF Last Updated 11 14 00 Page 6 of 166 ExpAssoc Function y y tA 1 e A 1 ag Brief Description Exponential associate Sample Curve y yO AI A2 offs ety 1 amplitud e A 1 width t7 1 amplitud e A 2 Parameters Number 5 Names y0 Al tl A2 t2 Meanings y0 offset Al amplitude t1 width A2 amplitude t2 width Initial Values yO 0 0 vary Al 1 0 vary t1 1 0 vary A2 1 0 vary t2 1 0 vary Lower Bounds tl gt 0 t2 gt 0 Upper Bounds none Script Access expassoc x y0 A1 t1 A2 t2 Function File FITFUNC EXPASSOC FDF Last Updated 11 14 00 Page 7 of 166 ExpDecay1 Function ya ys Agro Brief Description Exponential decay 1 with offset
20. Function A A A ge x log xo 1 10 Brief Description One site competition curve Dose response curve with Hill slope equal to 1 Sample Curve lA Top asymptate 41 10 Bottom asynptate A2 1 y ra OF AAT y 42 Parameters Number 3 Names A1 A2 log x0 Meanings Al top asymptote A2 bottom asymptote log x0 center Initial Values A1 10 0 vary A2 1 0 vary log x0 1 0 vary Lower Bounds none Upper Bounds none Script Access competition1 x A7 A2 LOGx0 Function File FITFUNC COMP1 FDF Last Updated 11 14 00 Page 117 of 166 TwoSiteBind Function Bui Bax 2X yc K x Kyte Brief Description Two site binding curve Sample Curve Bmaxi k 1 0 Me 20 ye k1 Ve Bm ae 14 Bmax ye Bmax 1 Him a2 Parameters Number 4 Names Bmaxl1 Bmax2 k1 k2 Meanings Bmax first top asymptote Bmax2 second top asymptote k1 first median k2 second median gm act 148m ac2 amp 2 Initial Values Bmaxl1 1 0 vary Bmax2 1 0 vary k1 1 0 vary k2 1 0 vary Lower Bounds none Upper Bounds none Script Access binding2 x Bmax1 Bmax2 k1 k2 Function File FITFUNC BIND2 FDF Last Updated 11 14 00 Page 118 of 166 TwoSiteComp Function A A f Ln A Xi f A y 2 1 10 xy 1 EP 1067s 39 Brief Description Two site competition Sample Curve Al OsFradionzl Topa de Al 10 First certer logo0 1 1 pas S
21. G 41 width wL 1 profile shape factor muz0 5 y y0 Parameters Number 6 Names y0 xc A wG wL mu Meanings y0 offset xc center A amplitude wG width wL width mu profile shape factor Initial Values y0 0 0 vary xc 0 0 vary A 1 0 vary wG 1 0 vary wL 1 0 vary mu 0 5 vary Lower Bounds wG gt 0 0 wL gt 0 0 Upper Bounds none Script Access psdvoigt2 x y0 xc A wG wL mu Function File FITFUNC PSDVGT2 FDF Last Updated 11 14 00 Page 161 of 166 Voigt Function 21n2 w e ges use s E 2 dt Ww X X 7 qi a aad Pes Wg Wg Brief Description Voigt peak function Sample Curve Al offset yYO 0 center xc 5 amplitud e A 1 wG 1 wL 1 Parameters Number 5 Names y0 xc A wG wL Meanings y0 offset xc center A amplitude wG Gaussian width wL Lorentzian width Initial Values yO 0 0 vary xc 0 0 vary A 1 0 vary wG 1 0 vary wL 1 0 vary Lower Bounds wG gt 0 0 wL gt 0 0 Upper Bounds none Script Access voigt5 x y0 xc A wG wL Function File FITFUNC VOIGTS FDF Last Updated 11 14 00 Page 162 of 166 12 Waveform Functions Sine 164 SineDamp 165 SineSqr 166 Last Updated 11 14 00 Page 163 of 166 Sine Function y Ass rd w Brief Description Sine function Sample Curve C enter xc 0 Widthw 1 IA Amplitude Az 1 xc 0 Parameters Number 3 Names xc w A Meanin
22. width A2 amplitude t2 width Initial Values yO 0 0 vary Al 1 0 vary t1 1 0 vary A2 1 0 vary t2 1 0 vary Lower Bounds tl gt 0 t2 gt 0 Upper Bounds none Script Access expassoc x y0 A1 t1 A2 t2 Function File FITFUNC EXPASSOC FDF Last Updated 11 14 00 Page 49 of 166 ExpDec1 Function y Aer Brief Description Exponential decay 1 Sample Curve offset yo 1 amplitude A 2 decay constant t 1 y yo Parameters Number 3 Names y0 A t Meanings y0 offset A amplitude t decay constant Initial Values yO 0 0 vary A 1 0 vary t 1 0 vary Lower Bounds none Upper Bounds none Script Access expdec1 x y0 A t Function File FITFUNC EXPDEC1 FDF Last Updated 11 14 00 Page 50 of 166 ExpDec2 Function x ty y y tAe A e Brief Description Exponential decay 2 Sample Curve offset yo 1 1 A1 t1 A2 t2 amplitude A1 1 decay constant t1 1 amplitude A2 2 decay constant t2 2 D yo A1 42 Parameters Number 5 Names y0 Al tl A2 t2 Meanings y0 offset Al amplitude t1 decay constant A2 amplitude t2 decay constant Initial Values yO 0 0 vary Al 1 0 vary t1 1 0 vary A2 1 0 vary t2 1 0 vary Lower Bounds none Upper Bounds none Script Access expdec2 x y0 A1 t1 A2 12 Function File FITFUNC EXPDEC2 FDF Last Updated 11 14 00 Page 51 of 166 ExpDec3 Function y 2yyt Ae
23. x Brief Description Hyperbola function Also the Michaelis Menten model in enzyme kinetics Sample Curve p1 p2 0 p121 p221 y p1ip2 xz p2 p120 52 0 p1 1 p2 1 yzp1 0 0 Parameters Number 2 Names P1 P2 Meanings P1 amplitude P2 unknown Initial Values P1 1 0 vary P2 1 0 vary Lower Bounds none Upper Bounds none Script Access hyperbl x P1 P2 Function File FITFUNC HYPERBL FDF Last Updated 11 14 00 Page 15 of 166 Logistic Function A A M Haut NND d xy C Brief Description Logistic dose response in pharmacology chemistry Sample Curve init alue A1 0 final value A271 center x0 5 y A2 power p 3 x1 0 p p 1 p x1 y1 D A1 Parameters Number 4 Names Al A2 x0 p Meanings A1 initial value A2 final value x0 center p power Initial Values A1 0 0 vary A2 1 0 vary x0 1 0 vary p 1 5 vary Lower Bounds p 0 0 Upper Bounds none Script Access logistic x A1 A2 x0 p Function File FITFUNC LOGISTIC FDF Last Updated 11 14 00 Page 16 of 166 LogNormal Function In xix F y Yo e 2w 27 wx Brief Description Log Normal function Sample Curve xc yO 4 Aw offset yO 0 center xc 150 width we0 3 arrplitude A 1 y0 Parameters Number 4 Names y0 xc w A Meanings y0 offset xc center w width A amplitude Initial Values y0 0 0 vary xc 1
24. x p4 x p2 0 0 Pppp Yp papi 5 Parameters Number 5 Names P1 P2 P3 P4 P5 Meanings Unknowns 1 5 Initial Values P1 1 0 vary P2 1 0 vary P3 1 0 vary P4 1 0 vary P5 1 0 vary Lower Bounds none Upper Bounds none Script Access dhyperbl x P1 P2 P3 P4 P5 Function File FITFUNC DHYPERBL FDF Last Updated 11 14 00 Page 82 of 166 Hyperbl Function __ Fix P x Brief Description Hyperbola function Also the Michaelis Menten model in enzyme kinetics Sample Curve p1 p2 0 p121 p221 y p1ip2 xz p2 p120 52 0 p1 1 p2 1 yzp1 0 0 Parameters Number 2 Names P1 P2 Meanings P1 amplitude P2 unknown Initial Values P1 1 0 vary P2 1 0 vary Lower Bounds none Upper Bounds none Script Access hyperbl x P1 P2 Function File FITFUNC HYPERBL FDF Last Updated 11 14 00 Page 83 of 166 HyperbolaGen Function b L q 1 cx Brief Description Generalized hyperbola function Reference Ratkowksy David A 1990 Handbook of Nonlinear Regression Models Marcel Dekker Inc 4 4 7 Sample Curve Tc Parameters Number 4 Names a b c d Meanings a coefficient b coefficient c coefficient d coefficient Initial Values a 1 0 vary b 1 0 vary c 0 5 d 0 5 Lower Bounds none Upper Bounds none Script Access hyperbolagen x a b c d Function File FITFUNC H YPE
25. y0 xc w A Function File FITFUNC GAUSSAMP FDF Last Updated 11 14 00 Page 100 of 166 GaussMod Function l w x x 2 A d oe do fo 2 t e J d e dy t oo 0 S c X X Ww where z Ww ty Brief Description Exponentially modified Gaussian peak function for use in chromatography Sample Curve offset y O armplitude A 1 center x width wel t 005 Ys Parameters Number 5 Names y0 A xc w tO Meanings y0 offset A amplitude xc center w width t0 unknown Initial Values yO 0 0 vary A 1 0 vary xc 0 0 vary w 1 0 vary t0 0 05 vary Lower Bounds w gt 0 0 t0 gt 0 0 Upper Bounds none Script Access gaussmod x y0 A xc w t0 Function File FITFUNC GAUSSMOD FDF Last Updated 11 14 00 Page 101 of 166 GCAS Function A i 212 4 a fi go quy ua wv 270 2 i pcs z Ww H 2 3z H z 62 3 Brief Description Gram Charlier peak function for use in chromatography Sample Curve offset yo 1 center xc 0 area A 1 width w 1 a3 0 01 a4 0 001 Parameters Number 6 Names yO xc A w a3 a4 Meanings y0 offset xc center A amplitude w width a3 unknown a4 unknown Initial Values yO 0 0 vary xc 0 0 vary A 1 0 vary w 1 0 vary a3 0 01 vary a4 0 001 vary Lower Bounds w 0 0 Upper Bounds none Script Access gcas x y0 xc A w a3
26. 0 Handbook of Nonlinear Regression Models Marcel Dekker Inc 4 3 32 Sample Curve Parameters Number 3 Names a b c Meanings a coefficient b coefficient c coefficient Initial Values a 1 0 vary b 1 0 vary c 0 5 Lower Bounds none Upper Bounds none Script Access log3p1 x a b c Function File FITFUNC LOG3P1 FDF Last Updated 11 14 00 Page 91 of 166 Logarithm Function y 2 In x A Brief Description One parameter logarithm Reference Ratkowksy David A 1990 Handbook of Nonlinear Regression Models Marcel Dekker Inc 4 1 1 Sample Curve y 1224 A 1 0 n C enter amp z1 Parameters Number 1 Names A Meanings A center Initial Values A 1 0 vary Lower Bounds none Upper Bounds none Script Access logarithm x A Function File FITFUNC LOGARITH FDF Last Updated 11 14 00 Page 92 of 166 7 Peak Functions Asym2Sig Beta CCE ECS Extreme Gauss GaussAmp GaussMod GCAS Giddings InvsPoly LogNormal Logistpk Lorentz PearsonVII PsdVoigtl PsdVoigt2 Voigt Weibull3 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 Last Updated 11 14 00 Page 93 of 166 Asym2Sig Function 1 1 y Yo T A x xo0w 2 x x w 2 l e l e Brief Description Asymmetric double sigmoidal Sample Curve A wl w2 w3 affset y 0 centerxc arrplitude A 1 widthw1 1 yy widthiw2 2 width
27. 0 vary w 1 0 vary A 1 0 vary Lower Bounds xc gt 0 w gt 0 Upper Bounds none Script Access lognormal x y0 xc w A Function File FITFUNC LOGNORM FDF Last Updated 11 14 00 Page 17 of 166 Lorentz Function 2A w Y Yo T A x x w Brief Description Lorentzian peak function Sample Curve xc yc yS OHA w pi Parameters Number 4 Names y0 xc w A Meanings y0 offset xc center w width A area Initial Values y0 0 0 vary xc 0 0 vary w 1 0 vary A 1 0 vary Lower Bounds w gt 0 0 Upper Bounds none Script Access lorentz x y0 xc w A Function File FITFUNC LORENTZ FDF Last Updated 11 14 00 Page 18 of 166 Pulse Function X Xg ti y y t A l e Brief Description Pulse function Sample Curve A t1 t2 0 y0 0 0ffset x0 0 center A 1 am plitude t120 5 width pz1 power 1220 5 width x1 2 x0 t1 In p t24t1 In t1 Parameters Number 6 Names y0 x0 A tl P t2 x1 y y0 Meanings y0 offset x0 center A amplitude t1 width P power t2 width Initial Values y0 0 0 vary x0 0 0 vary A 1 0 vary t1 1 0 vary P 1 0 vary t2 1 0 vary Lower Bounds A gt 0 0 tl gt 0 0 P gt 0 0 t2 gt 0 0 Upper Bounds none Script Access pulse x y0 x0 A t1 P t2 Function File FITFUNC PULSE FDF Last Updated 11 14 00 Page 19 of 166 RationalO Function
28. 43 of 166 Holliday1 Function a Wm M at bx cx Brief Description Extended Holliday model Sample Curve b 2c 4aci 4ac b xe b sqit b 4ac y2c 0 y 0 y 0 xe b sqrt b 4ac 2c Parameters Number 3 Names a b c Meanings a coefficient b coefficient c coefficient Initial Values a 1 0 vary b 1 0 vary c 0 5 Lower Bounds none Upper Bounds none Script Access holliday1 x a b c Function File FITFUNC HOLLIDY1 FDF Last Updated 11 14 00 Page 144 of 166 Nelder Function y x a by b x a b x ay Brief Description Nelder model a Yield fertilizer model in agriculture Sample Curve x1 a4 cb1 sqrtip 1 4b2 b 2b2 X2 a tb 1sqrti17 4b2 bIT 2b2 Xa fqrtibD b2 a X qrtbD bZ a Yu 7 Mtbt X 3 b1 Q b2 y 0 Geary LU b2 gt 0 an b2 0 p1 gt 0 b1 4 bO b2 0 b17 4b0 b2 gt 0 b1 b0 D 3 1 b0 2 bi93 b2 1 a 2 b0 1 bie2 b2 1 Parameters Number 4 Names a bO bl b2 Meanings a unknown b0 unknown b1 unknown b2 unknown Initial Values a 1 0 vary b0 1 0 vary b1 1 0 vary b2 1 0 vary Lower Bounds none Upper Bounds none Script Access nelder x a b0 b 1 b2 Function File FITFUNC NELDER FDF Last Updated 11 14 00 Page 145 of 166 RationalO Function b cx 1 ax Brief Description Rational function type 0 Reference Ratkowksy David A 1990 Handbook of Nonlinear Regression Mo
29. Curve Fitting Functions Contents 1 ORIGIN BASIC FUNCTIONS 5 eter Ree eee e e er eei esc MR ORE ENIM EROS 2 2 CHROMATOGRAPHY FUNCTIONS eese eene enne en nnsi einen AEN eate setas ente siens earn seras ennt 23 3 EXPONENTIAL FUNCTIONS eerie rere e redet eee Moe ee gues pese Pe e EAEE eene REL ei Taek 30 ENG e MIO OD P 69 5 HYPERBOLA FUNGTIONS tenni ori nie etenim RR On 81 GsLOGARITHM PUNCTIONS AE teet deett ete re D tret ite evade hl he tette 87 TSPEAK BUNCTIONS yee sede sers fase et trice ee e i ee re HERE bee E ERE Ta RH Eae e bones 93 8 PHARMACOLOGY FUNCTIONS eite hc c Piece idee e e coit ee ecd ESEE ERER R 113 9 POWER FUNCTIONS pis intrat i e rt dh EE dee a bi m i atii o tutis 120 TO RATIONAE FUNCTIONS enden RS NER I iei 140 11 SPECTROSCOPY FUNCTIONS tree tte tret ertt ree Pee Eae Eee stretta pee rente Pede re eiae se eara nee 155 12 WAVEFORM FUNCTIONS eter MIR P Rees More eee pepe ee pida cei eser eee es R E E P Re ieee Si 163 Last Updated 11 14 00 Page 1 of 166 1 Origin Basic Functions Allometricl Beta Boltzmann Dhyperbl ExpAssoc ExpDecayl ExpDecay2 ExpDecay3 ExpGrowl ExpGrow2 Gauss GaussAmp Hyperbl Logistic LogNormal Lorentz Pulse RationalO Sine Voigt Last Updated 11 14 00 Page 2 of 166 Allometric1 Function b y ax Brief Description Classical Freundlich model Has been used in the study of allometry Sample Curve y arb Parameters Numb
30. Marcel Dekker Inc 3 3 7 Sample Curve Parameters Number 2 Names a b Meanings a unknown b unknown Initial Values a 1 0 vary b 1 0 vary Lower Bounds none Upper Bounds none Script Access bradley x a b Function File FITFUNC BRADLEY FDF Last Updated 11 14 00 Page 88 of 166 Log2P1 Function y bln x a Brief Description Two parameter logarithm function Reference Ratkowksy David A 1990 Handbook of Nonlinear Regression Models Marcel Dekker Inc 4 2 1 Sample Curve x a a 1 0 y b Parameters Number 2 Names a b Meanings a offset b coefficient Initial Values a 1 0 vary b 1 0 vary Lower Bounds none Upper Bounds none Script Access log2p1 x a b Function File FITFUNC LOG2P1 FDF Last Updated 11 14 00 Page 89 of 166 Log2P2 Function y In a bx Brief Description Two parameter logarithm Reference Ratkowksy David A 1990 Handbook of Nonlinear Regression Models Marcel Dekker Inc 4 2 3 Sample Curve x aih Parameters Number 2 Names a b Meanings a offset b coefficient Initial Values a 1 0 vary b 1 0 vary Lower Bounds none Upper Bounds none Script Access log2p2 x a b Function File FITFUNC LOG2P2 FDF Last Updated 11 14 00 Page 90 of 166 Log3P1 Function y a bln x c Brief Description Three parameter logarithm function Reference Ratkowksy David A 199
31. Models Marcel Dekker Inc 4 2 10 Sample Curve Pab a5 raet 2 5 Oa y Parameters Number 2 Names a b Meanings a coefficient b rate Initial Values a 1 0 vary b 1 5 vary Lower Bounds none Upper Bounds none Script Access exp2pmod1 x a b Function File FITFUNC EXP2PMD1 FDF Last Updated 11 14 00 Page 44 of 166 Exp2PMod2 Function at bx y e Brief Description Two parameter exponential function Reference Ratkowksy David A 1990 Handbook of Nonlinear Regression Models Marcel Dekker Inc 42 11 a 3 rate b 15 y 0 y Sample Curve a 3 rateb 15 y j b y Ca h taht Parameters Number 2 Names a b Meanings a coefficient b rate Initial Values a 1 0 vary b 1 5 vary Lower Bounds none Upper Bounds none Script Access exp2pmod2 x a b Function File FITFUNC EXP2PMD2 FDF Last Updated 11 14 00 Page 45 of 166 Exp3P1 Function b y ae Brief Description Three parameter exponential function Reference Ratkowksy David A 1990 Handbook of Nonlinear Regression Models Marcel Dekker Inc 4 3 33 Sample Curve Parameters Number 3 Names a b c Meanings a coefficient b coefficient c coefficient Initial Values a 1 0 vary b 1 0 vary c 0 5 Lower Bounds none Upper Bounds none Script Access exp3p1 x a b c Function File FITFUNC EXP3P1 FDF Last Updated 11 14 00 Page 46 of 166
32. NC MMOLECU FDF Last Updated 11 14 00 Page 63 of 166 MnMolecular1 Function y A Ae Brief Description Monomolecular growth model Reference Seber G A F Wild C J 1989 Nonlinear Regression John Wiley amp Sons Inc p 328 Sample Curve yA 0 A pA 9 y 7K A yA Parameters Number 3 Names Al A2 k Meanings Al offset A2 coefficient k coefficient Initial Values A1 1 0 vary A2 1 0 vary k 1 0 vary Lower Bounds A1 gt 0 0 A2 gt 0 0 Upper Bounds none Script Access mnmolecular1 x A1 A2 k Function File FITFUNC MMOLECU1 FDF Last Updated 11 14 00 Page 64 of 166 Shah Function y a bx cr Brief Description Shah model Sample Curve offset a 1 hz1 x In b c Into yin r y 7a b x c y b c In r Parameters Number 4 Names a b c r Meanings a offset b coefficient c coefficient r unknown Initial Values a 1 0 vary b 1 0 vary c 1 0 vary r 0 5 vary Lower Bounds r 0 0 Upper Bounds r 1 0 Script Access shah x a b c r Function File FITFUNC SHAH FDF Last Updated 11 14 00 Page 65 of 166 Stirling Function e 1 a b k Brief Description Stirling model Sample Curve seabk Offset a 1 yb ua b 1 it y k 1 08 yza hik Parameters Number 3 Names a b k Meanings a offset b coefficient k coefficient Initial Values a 1 0 var
33. RGEN FDF Last Updated 11 14 00 Page 84 of 166 HyperbolaMod Function X lT 8x46 Brief Description Modified hyperbola function Reference Ratkowksy David A 1990 Handbook of Nonlinear Regression Models Marcel Dekker Inc 4 2 18 Sample Curve THOSTHOS A ACTZTtsqKDyTIATI4sqKTZ T BCT2THsqi T2VTA A Ttsqii T2 T4 Parameters Number 2 Names T1 T2 Meanings T1 amplitude T2 unknown Initial Values T1 1 0 vary T2 1 0 vary Lower Bounds none Upper Bounds none Script Access hyperbolamod x T1 T2 Function File FITFUNC HYPERBMD FDF Last Updated 11 14 00 Page 85 of 166 RectHyperbola Function bx 1 bx y a Brief Description Rectangular hyperbola function Reference Ratkowksy David A 1990 Handbook of Nonlinear Regression Models Marcel Dekker Inc 4 2 16 Sample Curve ab gt 0 Parameters Number 2 Names a b Meanings a coefficient b coefficient Initial Values a 1 0 vary b 1 0 vary Lower Bounds none Upper Bounds none Script Access recthyperbola x a b Function File FITFUNC RECTHYPB FDF Last Updated 11 14 00 Page 86 of 166 6 Logarithm Functions Bradley Log2P1 Log2P2 Log3P1 Logarithm 88 89 90 91 92 Last Updated 11 14 00 Page 87 of 166 Bradley Function y 2 aln bIn x Brief Description Bradley model Reference Ratkowksy David A 1990 Handbook of Nonlinear Regression Models
34. Wild C J 1989 Nonlinear Regression John Wiley amp Sons Inc pp 338 339 Sample Curve FA Gd YD Pog 0 Y 0Y Oen Gen ed xf xd Parameters Number 4 Names A xc d k Meanings A amplitude xc center d power k coefficient Initial Values A 1 0 vary xc 1 0 vary d 5 0 vary k 1 0 vary Lower Bounds A gt 0 0 k gt 0 0 Upper Bounds none Script Access sweibull1 x A xc d k Function File FITFUNC WEIBULL1 FDF Last Updated 11 14 00 Page 79 of 166 SWeibull2 Function y A A Be Brief Description Sigmoidal Weibull function type 2 Reference Seber G A F Wild C J 1989 Nonlinear Regression John Wiley amp Sons Inc pp 338 330 Sample Curve y A xfAd 1ytd W 0B Parameters Number 4 Names a b d k Meanings a unknown b unknown d power k coefficient Initial Values a 1 0 vary b 1 0 vary d 5 0 vary k 1 0 vary Lower Bounds a 0 0 b gt 0 0 k gt 0 0 Upper Bounds none Script Access sweibull2 x a b d k Function File FITFUNC WEIBULL2 FDF Last Updated 11 14 00 Page 80 of 166 5 Hyperbola Functions Dhyperbl Hyperbl HyperbolaGen HyperbolaMod RectHyperbola 82 83 84 85 86 Last Updated 11 14 00 Page 81 of 166 Dhyperbl Function __ Bx Ex Ptx P x y Px Brief Description Double rectangular hyperbola function Sample Curve PIRA ng p4 2 p6 5 xp
35. a b c Function File FITFUNC FRENDEXT FDF Last Updated 11 14 00 Page 127 of 166 Gunary Function y X at bx4 cv x Brief Description Gunary model Sample Curve y 1b AIH 840 Scia 1 1 a4b d ecl b 1 0 0 c 05 Parameters Number 3 Names a b c Meanings a coefficient b coefficient c coefficient Initial Values a 1 0 vary b 1 0 vary c 0 5 Lower Bounds none Upper Bounds none Script Access gunary x a b c Function File FITFUNC GUNARY FDF Last Updated 11 14 00 Page 128 of 166 Harris Function y a bx Brief Description Farazdaghi Harris model for use in yield density study Sample Curve power cz0 5 D 1 2 1 1 ab y b cKa eby 1 xl y brei asb zs xl a b Parameters Number 3 Names a b c Meanings a coefficient b coefficient c power Initial Values a 1 0 vary b 1 0 vary c 0 5 Lower Bounds none Upper Bounds none Script Access harris x a b c Function File FITFUNC HARRIS FDF Last Updated 11 14 00 Page 129 of 166 LangmuirEXT1 Function 1 c abx n sbx Brief Description Extended Langmuir model Sample Curve yP arb 1 cy 1 1 2 bi 14 0 0 Parameters Number 3 Names a b c Meanings a coefficient b coefficient c coefficient Initial Values a 1 0 vary b 1 0 vary c 0 5 Lower Bounds none Upper Bounds none Script Access lang
36. a4 Function File FITFUNC GRMCHARL FDF Last Updated 11 14 00 Page 102 of 166 Giddings Function A x 2r yer L li Ww X Ww Brief Description Giddings peak function for use in chromatography Sample Curve offset y 1 center 5 width we1 area A Parameters Number 4 Names y0 xc w A Meanings y0 offset xc center w width A area Initial Values yO 0 0 vary xc 1 0 vary w 1 0 vary A 1 0 vary Lower Bounds w gt 0 0 Upper Bounds none Script Access giddings x yO xc w A Function File FITFUNC GIDDINGS FDF Last Updated 11 14 00 Page 103 of 166 InvsPoly Function A peg 2 4 6 afa Zo er 2 Ww Ww Ww Brief Description Inverse polynomial peak function with center Sample Curve R22D0D w l w2D 4 n AsO AZO AsO Aico RZ hAZ 34A1 A3 U yU D xce1 w 5 y U xce 1 5 A2 3 A1 A3 nD A10 AJ gt 0 Restated Asi Aisi yO 0 xcs 1 5 AZ 1 A3 1 AZe1 A3 41 A 1 A 1e1 AZ 3 A3 7 3 y y 0 yoo Parameters Number 7 Names y0 xc w A Al A2 A3 Meanings y0 offset xc center w width A amplitude Al coefficient A2 coefficient A3 coefficient Initial Values yO 0 0 vary xc 0 0 vary w 1 0 vary A 1 0 vary Al 0 0 vary A2 0 0 vary A3 0 0 vary Lower Bounds w gt 0 0 Al 2 0 0 A2 gt 0 0 A32 0 0 Upper Bounds none Script Access invspoly x y0 xc w A A1 A2 A3
37. age 158 of 166 PearsonVIl Function 1 mu 4 2 mu ore 5 i i phim y mu y X X n eU om 1 2 w c Brief Description Pearson VII peak function Sample Curve X XC y 0 y 0 Parameters Number 4 Names xc A w mu Meanings xc center A amplitude w width mu profile shape factor Initial Values xc 0 0 vary A 1 0 vary w 1 0 vary mu 1 0 vary Lower Bounds A gt 0 0 w gt 0 0 mu gt 0 0 Upper Bounds none Script Access pearsonvii x xc A w mu Function File FITFUNC PEARSON7 FDF Last Updated 11 14 00 Page 159 of 166 PsdVoigt1 Function za na x x y zudem s 4 x x w Jaw 2 Y Yo Al m T Brief Description Pseudo Voigt peak function type 1 Sample Curve yaso E width w 71 profile shape factor mu 0 5 y y0 Parameters Number 5 Names y0 xc A w mu Meanings y0 offset xc center A amplitude w width mu profile shape factor Initial Values y0 0 0 vary xc 0 0 vary A 1 0 vary w 1 0 vary mu 0 5 vary Lower Bounds w gt 0 0 Upper Bounds none Script Access psdvoigt1 x y0 xc A w mu Function File FITFUNC PSDVGT1 FDF Last Updated 11 14 00 Page 160 of 166 PsdVoigt2 Function 4l 2 w 44112 7 2 67 Y Yo Alm 2 2 a e 4 x x w Jaw Brief Description Pseudo Voigt peak function type 2 Sample Curve x xc yl1 20 center xc 0 amplitude A 1 width w
38. cas1 x a b Function File FITFUNC BOXLUC1 FDF Last Updated 11 14 00 Page 32 of 166 BoxLucas1Mod Function y all p Brief Description A parameterization of Box Lucas model Reference Ratkowksy David A 1990 Handbook of Nonlinear Regression Models Marcel Dekker Inc 4 3 5 Sample Curve y a par C x en 0 0 y 1 a In b Parameters Number 2 Names a b Meanings a coefficient b coefficient Initial Values a 1 0 vary b 1 0 vary Lower Bounds none Upper Bounds none Script Access boxlucas1mod x a b Function File FITFUNC BOXLCIMD FDF Last Updated 11 14 00 Page 33 of 166 BoxLucas2 Function y a gn _ ew a a Brief Description A parameterization of Box Lucas model Reference Seber G A F Wild C J 1989 Nonlinear Regression John Wiley amp Sons Inc p 254 Sample Curve Parameters Number 2 Names al a2 Meanings al unknown a2 unknown Initial Values al 2 0 vary a2 1 0 vary Lower Bounds none Upper Bounds none Script Access boxlucas2 x a1 a2 Function File FITFUNC BOXLUC2 FDF Last Updated 11 14 00 Page 34 of 166 Chapman Function y al e y Brief Description Chapman model Reference Ratkowksy David A 1990 Handbook of Nonlinear Regression Models Marcel Dekker Inc 4 3 35 Sample Curve 0 0 y 2 0 Parameters Number 3 Names a b c Meanings a coefficient b coeffi
39. cient c coefficient Initial Values a 1 0 vary b 1 0 vary c 0 5 Lower Bounds none Upper Bounds none Script Access chapman x a b c Function File FITFUNC CHAPMAN FDF Last Updated 11 14 00 Page 35 of 166 Exp1P1 Function x A y e Brief Description One parameter exponential function Reference Ratkowksy David A 1990 Handbook of Nonlinear Regression Models Marcel Dekker Inc 4 1 5 Sample Curve 1 1 position A 1 y A 1 y 0 Parameters Number 1 Names A Meanings A position Initial Values A 1 0 vary Lower Bounds none Upper Bounds none Script Access exp1p1 x A Function File FITFUNC EXP1P1 FDF Last Updated 11 14 00 Page 36 of 166 Exp1p2 Function Ax y e Brief Description One parameter exponential function Reference Ratkowksy David A 1990 Handbook of Nonlinear Regression Models Marcel Dekker Inc 4 1 15 Sample Curve Parameters Number 1 Names A Meanings A coefficient Initial Values A 1 0 vary Lower Bounds none Upper Bounds none Script Access exp1p2 x A Function File FITFUNC EXP1P2 FDF Last Updated 11 14 00 Page 37 of 166 Exp1p2md Function y B Brief Description One parameter exponential function Reference Ratkowksy David A 1990 Handbook of Nonlinear Regression Models Marcel Dekker Inc 4 1 16 Sample Curve Parameters Number 1 Names B Meanings B pos
40. cription One parameter linear reciprocal function Sample Curve Parameters Number 1 Names A Meanings A position Initial Values A 1 0 vary Lower Bounds none Upper Bounds none Script Access reciprocal1 x A Function File FITFUNC RECIPR1 FDF Last Updated 11 14 00 Page 153 of 166 ReciprocalMod Function a 1 bx y Brief Description Two parameter linear reciprocal function Sample Curve a 1 a 1 h 1 b 1 Parameters Number 2 Names a b Meanings a coefficient b coefficient Initial Values a 1 0 vary b 1 0 vary Lower Bounds none Upper Bounds none Script Access reciprocalmod x a b Function File FITFUNC RECIPMOD FDF Last Updated 11 14 00 Page 154 of 166 11 Spectroscopy Functions GaussAmp InvsPoly Lorentz PearsonVII PsdVoigtl PsdVoigt2 Voigt 156 157 158 159 160 161 162 Last Updated 11 14 00 Page 155 of 166 GaussAmp Function 2 x x y 2w y y Ae Brief Description Amplitude version of Gaussian peak function Sample Curve 2w wiisqrt In 4 xe yOrA Faw gt O offset yO 0 center xc 0 width w 1 amplitude A 10 Parameters Number 4 Names y0 xc w A Meanings y0 offset xc center w width A area Initial Values yO 0 0 vary xc 0 0 vary w 1 0 vary A 10 vary Lower Bounds w gt 0 0 Upper Bounds none Script Access gaussamp x y0 xc w A F
41. dels Marcel Dekker Inc 4 3 24 Sample Curve Parameters Number 3 Names a b c Meanings a coefficient b coefficient c coefficient Initial Values a 1 0 vary b 1 0 vary c 0 5 Lower Bounds none Upper Bounds none Script Access rational0 x a b c Function File FITFUNC RATIONO FDF Last Updated 11 14 00 Page 146 of 166 Rational1 Function ELI a 4 bx Brief Description Rational function type 1 Sample Curve Parameters Number 3 Names a b c Meanings a coefficient b coefficient c coefficient Initial Values a 1 0 vary b 1 0 vary c 0 5 Lower Bounds none Upper Bounds none Script Access rational1 x a b c Function File FITFUNC RATION1 FDF Last Updated 11 14 00 Page 147 of 166 Rational2 Function bt cx at x Brief Description Rational function type 2 Sample Curve Parameters Number 3 Names a b c Meanings a coefficient b coefficient c coefficient Initial Values a 1 0 vary b 1 0 vary c 0 5 Lower Bounds none Upper Bounds none Script Access rational2 x a b c Function File FITFUNC RATION2 FDF Last Updated 11 14 00 Page 148 of 166 Rational3 Function dae a T cx Brief Description Rational function type 3 Sample Curve Parameters Number 3 Names a b c Meanings a coefficient b coefficient c coefficient Initial Values a 1 0 vary b
42. eber G A F Wild C J 1989 Nonlinear Regression John Wiley amp Sons Inc p 298 Sample Curve y pjp p 0 p p Xato Parameters Number 4 Names pl p2 p3 p4 Meanings p1 coefficient p2 unknown p3 offset p4 coefficient Initial Values p1 1 0 vary p2 1 0 vary p3 1 0 vary p4 1 0 vary Lower Bounds none Upper Bounds none Script Access explinear x p1 p2 p3 p4 Function File FITFUNC EXPLINEA FDF Last Updated 11 14 00 Page 61 of 166 Exponential Function Rox y y Ae Brief Description Exponential Sample Curve Parameters Number 3 Names y0 A RO Meanings y0 offset A initial value RO rate Initial Values yO 0 0 vary A 1 0 vary RO 1 0 vary Lower Bounds A gt 0 0 Upper Bounds none Script Access exponential x yO A RO Function File FITFUNC EXPONENT FDF Last Updated 11 14 00 Page 62 of 166 MnMolecular Function y Afi ete Brief Description Monomolecular growth model Reference Seber G A F Wild C J 1989 Nonlinear Regression John Wiley amp Sons Inc p 328 Sample Curve yA EA 0 0 ep ye FA Parameters Number 3 Names A xc k Meanings A amplitude xc center k rate Initial Values A 2 0 vary xc 1 0 vary k 1 0 vary Lower Bounds A gt 0 0 Upper Bounds none Script Access mnmolecular x A xc k Function File FITFU
43. econd center log J Fradiorp5 Batomasyrrptote 2 1 Parameters Number 5 Names Al A2 log x0 1 log x0_2 f Meanings Al top asymptote A2 bottom asymptote log xO 1 first center log x0 2 second center f fraction Initial Values A1 10 0 vary A2 1 0 vary log xO 1 1 0 vary log x0_2 2 0 vary f 0 5 vary Lower Bounds none Upper Bounds none Script Access competition2 x A7 A2 LOGx0_1 LOGx0_2 f Function File FITFUNC COMP2 FDF Last Updated 11 14 00 Page 119 of 166 9 Power Functions Allometricl Allometric2 Asym2Sig Belehradek BINeld BlNeldSmp FreundlichEXT Gunary Harris LangmuirEXT1 LangmuirEXT2 Pareto Pow2P1 Pow2P2 Pow2P3 Power PowerO Powerl Power2 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 Last Updated 11 14 00 Page 120 of 166 Allometric1 Function b y ax Brief Description Classical Freundlich model Has been used in the study of allometry Sample Curve az1 b 0 07 power b 10 y a b Parameters Number 2 Names a b Meanings a coefficient b power Initial Values a 1 0 vary b 0 5 vary Lower Bounds none Upper Bounds none Script Access allometric1 x a b Function File FITFUNC ALLOMET1 FDF Last Updated 11 14 00 Page 121 of 166 Allometric2 Function y a cbx Brief Description An extension of classical Freundlich model Sample Cu
44. ent Initial Values A 1 0 vary Lower Bounds none Upper Bounds none Script Access exp1p4 x A Function File FITFUNC EXP1P4 FDF Last Updated 11 14 00 Page 41 of 166 Exp1P4Md Function y 1 B Brief Description One parameter exponential function Reference Ratkowksy David A 1990 Handbook of Nonlinear Regression Models Marcel Dekker Inc 4 1 19 Sample Curve Parameters Number 1 Names B Meanings B coefficient Initial Values B 1 0 vary Lower Bounds none Upper Bounds none Script Access exp1p4md x B Function File FITFUNC EXP1P4 FDF Last Updated 11 14 00 Page 42 of 166 Exp2P Function y ab Brief Description Two parameter exponential function Reference Ratkowksy David A 1990 Handbook of Nonlinear Regression Models Marcel Dekker Inc 4 2 9 Sample Curve y position a 1 m i em postion a 1 position b 2 nb TU postion b 0 5 position a 1 y in hi postion 1 position b 2 Qa y ban a position b 0 5 0 yD Parameters Number 2 Names a b Meanings a position b position Initial Values a 1 0 vary b 1 5 vary Lower Bounds none Upper Bounds none Script Access exp2p x a b Function File FITFUNC EXP2P FDF Last Updated 11 14 00 Page 43 of 166 Exp2PMod1 Function bx y ae Brief Description Two parameter exponential function Reference Ratkowksy David A 1990 Handbook of Nonlinear Regression
45. er 2 Names a b Meanings a coefficient b power Initial Values a 1 0 vary b 0 5 vary Lower Bounds none Upper Bounds none Script Access allometric1 x a b Function File FITFUNC ALLOMET1 FDF Last Updated 11 14 00 Page 3 of 166 Beta Function w5 l w3 1 NET W tw 2 x x iis w w 2 x x w 1 w w 1 w Brief Description The beta function Sample Curve x1 xc w2 1 w1 w2 w3 2 x2 xc w3 1 w1 w2 w3 2 xc yO A A20 offsety0 0 y oo y0 center xc 8 amplitude A 1 W1 15 w2 3 w3 4 Parameters Number 6 Names yO xc A wl w2 w3 Meanings y0 offset xc center A amplitude wl width w2 width w3 width Initial Values y0 0 0 vary xc 1 0 vary A 5 0 vary wl 5 0 vary w2 2 0 vary w3 2 0 vary Lower Bounds wl gt 0 0 w2 gt 1 0 w3 gt 1 0 Upper Bounds none Script Access beta x y0 xc A w1 w2 w3 Function File FITFUNC BETA FDF Last Updated 11 14 00 Page 4 of 166 Boltzmann Function __A A A Pc x xy dx 2 l e Brief Description Boltzmann function produces a sigmoidal curve Sample Curve y A2 init value A120 final value A2 21 center x0 0 time constdx 1 x0 A1 A 23 2 y A 2 A 1 4 dx y A1 Parameters Number 4 Names Al A2 x0 dx Meanings A1 initial value A2 final value x0 center dx time constant Initial Values A1 0 0 vary
46. ffset x0 center Al amplitude t1 decay constant A2 amplitude t2 decay constant Initial Values yO 0 0 vary x0 0 0 vary Al 10 vary t1 1 0 vary A2 10 vary t2 1 0 vary Lower Bounds none Upper Bounds none Script Access expdecay2 x y0 x0 A1 t1 A2 t2 Function File FITFUNC EXPDECY 2 FDF Last Updated 11 14 00 Page 54 of 166 ExpDecay3 Function y Yo Ae o 4 Ae 07 Aye Ct Brief Description Exponential decay 3 with offset Sample Curve 0 y 0 A1 A 2 3 center x0 2 A1210 A 2210 A3 5 t121 122213 3 Y A1 t1 A2 t2 A3 t3 Parameters Number 8 Names y0 x0 Al tl A2 t2 A3 t3 Meanings y0 offset xO center Al amplitude t1 decay constant A2 amplitude t2 decay constant A3 amplitude t3 decay constant Initial Values yO 0 0 vary x0 0 0 vary Al 10 vary tl 1 0 vary A2 10 vary t2 1 0 vary A3 10 vary t3 1 0 vary Lower Bounds none Upper Bounds none Script Access expdecay3 x y0 x0 A 1 t1 A2 12 A3 13 Function File FITFUNC EXPDECY3 FDF Last Updated 11 14 00 Page 55 of 166 ExpGro1 Function xit y y t Ae Brief Description Exponential growth 1 Sample Curve offset yo 1 amplitude A4 1 t1 1 A1 t1 y yO Parameters Number 3 Names y0 Al tl Meanings y0 offset Al amplitude t1 growth constant Initial Values yO 0 0 vary Al 1 0 vary t1
47. ge 109 of 166 PsdVoigt2 Function 4l 2 w 44112 7 2 67 Y Yo Alm 2 2 a e 4 x x w Jaw Brief Description Pseudo Voigt peak function type 2 Sample Curve x xc yl1 20 center xc 0 amplitude A 1 width w G 41 width wL 1 profile shape factor muz0 5 y y0 Parameters Number 6 Names y0 xc A wG wL mu Meanings y0 offset xc center A amplitude wG width wL width mu profile shape factor Initial Values y0 0 0 vary xc 0 0 vary A 1 0 vary wG 1 0 vary wL 1 0 vary mu 0 5 vary Lower Bounds wG gt 0 0 wL gt 0 0 Upper Bounds none Script Access psdvoigt2 x y0 xc A wG wL mu Function File FITFUNC PSDVGT2 FDF Last Updated 11 14 00 Page 110 of 166 Voigt Function 21n2 w e ges use s E 2 dt Ww X X 7 qi a aad Pes Wg Wg Brief Description Voigt peak function Sample Curve Al offset yYO 0 center xc 5 amplitud e A 1 wG 1 wL 1 Parameters Number 5 Names y0 xc A wG wL Meanings y0 offset xc center A amplitude wG Gaussian width wL Lorentzian width Initial Values yO 0 0 vary xc 0 0 vary A 1 0 vary wG 1 0 vary wL 1 0 vary Lower Bounds wG gt 0 0 wL gt 0 0 Upper Bounds none Script Access voigt5 x y0 xc A wG wL Function File FITFUNC VOIGTS FDF Last Updated 11 14 00 Page 111 of 166 Weibull3 Function m i ppa C Brief Descriptio
48. gs xc center w width A amplitude Initial Values xc 0 0 vary w 1 0 vary A 1 0 vary Lower Bounds w gt 0 Upper Bounds none Script Access sine x xc w A Function File FITFUNC SINE FDF Last Updated 11 14 00 Page 164 of 166 SineDamp Function X m x x y Ae sin z w Brief Description Sine damp function Sample Curve center xc 5 wWidthiwe decay constant t0 10 amplitude A 5 Parameters Number 4 Names xc w t0 A Meanings xc center w width t0 decay constant A amplitude Initial Values xc 0 0 vary w 1 0 vary t0 1 0 vary A 1 0 vary Lower Bounds w gt 0 0 t0 gt 0 0 Upper Bounds none Script Access sinedamp x xc w t0 A Function File FITFUNC SINEDAMP FDF Last Updated 11 14 00 Page 165 of 166 SineSqr Function y EL EK w Brief Description Sine square function Sample Curve xc w2 A A2 s I amplitude A 1 w2 xc Parameters Number 3 Names xc w A Meanings xc center w width A amplitude Initial Values xc 0 0 vary w 1 0 vary A 1 0 vary Lower Bounds w gt 0 0 Upper Bounds none Script Access sinesqr x xc w A Function File FITFUNC SINESQR FDF Last Updated 11 14 00 Page 166 of 166
49. h A area Initial Values y0 0 0 vary xc 0 0 vary w 1 0 vary A 1 0 vary Lower Bounds w gt 0 0 Upper Bounds none Script Access lorentz x y0 xc w A Function File FITFUNC LORENTZ FDF Last Updated 11 14 00 Page 107 of 166 PearsonVIl Function 1 mu 4 2 mu ore 5 i i phim y mu y X X n eU om 1 2 w c Brief Description Pearson VII peak function Sample Curve X XC y 0 y 0 Parameters Number 4 Names xc A w mu Meanings xc center A amplitude w width mu profile shape factor Initial Values xc 0 0 vary A 1 0 vary w 1 0 vary mu 1 0 vary Lower Bounds A gt 0 0 w gt 0 0 mu gt 0 0 Upper Bounds none Script Access pearson7 x xc A w mu Function File FITFUNC PEARSON7 FDF Last Updated 11 14 00 Page 108 of 166 PsdVoigt1 Function za na x x y zudem s 4 x x w Jaw 2 Y Yo Al m T Brief Description Pseudo Voigt peak function type 1 Sample Curve yaso E width w 71 profile shape factor mu 0 5 y y0 Parameters Number 5 Names y0 xc A w mu Meanings y0 offset xc center A amplitude w width mu profile shape factor Initial Values y0 0 0 vary xc 0 0 vary A 1 0 vary w 1 0 vary mu 0 5 vary Lower Bounds w gt 0 0 Upper Bounds none Script Access psdvoigt1 x y0 xc A w mu Function File FITFUNC PSDVGT1 FDF Last Updated 11 14 00 Pa
50. ipt Access slogistic1 x a xc k Function File FITFUNC SLOGIST1 FDF Last Updated 11 14 00 Page 74 of 166 SLogistic2 Function a 14 a Yo e Vraa Yo Brief Description Sigmoidal logistic function type 2 Reference Seber G A F Wild C J 1989 Nonlinear Regression John Wiley amp Sons Inc pp 328 330 Sample Curve y a Oc 4w y0 a y0 a y 0 Parameters Number 3 Names y0 a Wmax Meanings y0 initial value a amplitude Wmax maximum growth rate Initial Values yO 0 5 vary a 1 0 vary Wmax 1 0 vary Lower Bounds y0 gt 0 0 a gt 0 0 Wmax gt 0 0 Upper Bounds none Script Access slogistic2 x y0 a Wmax Function File FITFUNC SLOGIST2 FDF Last Updated 11 14 00 Page 75 of 166 SLogistic3 Function a dim 1 be Brief Description Sigmoidal logistic function type 3 Reference Seber G A F Wild C J 1989 Nonlinear Regression John Wiley amp Sons Inc pp 328 330 Sample Curve y a y 1 2a k 4 y 2 xO a 2 b exp k x0 1 oy a 1 b 1 ke Parameters Number 3 Names a b k Meanings a amplitude b coefficient k coefficient Initial Values a 1 0 vary b 1 0 vary k 1 0 vary Lower Bounds a gt 0 0 b gt 0 0 k gt 0 0 Upper Bounds none Script Access slogistic3 x a b k Function File FITFUNC SLOGIST3 FDF Last Updated 11 14 00 Page 76 of 166 SRichards1 Function
51. ition Initial Values B 1 0 vary Lower Bounds none Upper Bounds none Script Access exp1p2md x B Function File FITFUNC EXP1P2MD FDF Last Updated 11 14 00 Page 38 of 166 Exp1p3 Function y Ae Brief Description One parameter exponential function Reference Ratkowksy David A 1990 Handbook of Nonlinear Regression Models Marcel Dekker Inc 4 1 13 Sample Curve y 0 Parameters Number 1 Names A Meanings A coefficient Initial Values A 1 0 vary Lower Bounds none Upper Bounds none Script Access exp1p3 x A Function File FITFUNC EXP1P3 FDF Last Updated 11 14 00 Page 39 of 166 Exp1P3Md Function y In B B Brief Description One parameter exponential function Reference Ratkowksy David A 1990 Handbook of Nonlinear Regression Models Marcel Dekker Inc 4 1 14 Sample Curve y 0 D In B y In B Parameters Number 1 Names B Meanings B coefficient Initial Values B 5 0 vary Lower Bounds none Upper Bounds none Script Access exp1p3md x B Function File FITFUNC EXP1P3MD DFD Last Updated 11 14 00 Page 40 of 166 Exp1P4 Function Ax y l e Brief Description One parameter exponential function Reference Ratkowksy David A 1990 Handbook of Nonlinear Regression Models Marcel Dekker Inc 4 1 18 Sample Curve y 1 0 0 Parameters Number 1 Names A Meanings A coeffici
52. iw3 3 Parameters Number 6 Names yO xc A wl w2 w3 Meanings y0 offset xc center A amplitude wl width w2 width w3 width Initial Values yO 0 0 vary xc 0 0 vary A 1 0 vary w1 1 0 vary w2 1 0 vary w3 1 0 vary Lower Bounds wl gt 0 0 w2 gt 0 0 w3 gt 0 0 Upper Bounds none Script Access asym2sig x y0 xc A w1 w2 w3 Function File FITFUNC AS YMDBLS FDF Last Updated 11 14 00 Page 94 of 166 Beta Function w5 l w3 1 NET W tw 2 x x iis w w 2 x x w 1 w w 1 w Brief Description The beta function Sample Curve x1 xc w2 1 w1 w2 w3 2 x2 xc w3 1 w1 w2 w3 2 xc yO A A20 offsety0 0 y Nga y0 center xc 8 amplitude A 1 W1 15 w2 3 w3 4 Parameters Number 6 Names yO xc A wl w2 w3 Meanings y0 offset xc center A amplitude wl width w2 width w3 width Initial Values y0 0 0 vary xc 1 0 vary A 5 0 vary wl 5 0 vary w2 2 0 vary w3 2 0 vary Lower Bounds wl gt 0 0 w2 gt 1 0 w3 gt 1 0 Upper Bounds none Script Access beta x y0 xc A w1 w2 w3 Function File FITFUNC BETA FDF Last Updated 11 14 00 Page 95 of 166 CCE Function xx y y y tAle B 1 0 5 1 tanh k x xe e 9 67097 Brief Description Chesler Cram peak function for use in chromatography Sample Curve offs et y 0 Keg Xag 12 3 A 1 Paramete
53. muirext1 x a b c Function File FITFUNC LANGEXT1 FDF Last Updated 11 14 00 Page 130 of 166 LangmuirEXT2 Function 1 ye a bx Brief Description Extended Langmuir model Sample Curve Ti cc 1 x a b yz1 a 1 ath Aag 1 184b y b 1 cy a by y b 1 c asb Parameters Number 3 Names a b c Meanings a coefficient b coefficient c coefficient Initial Values a 1 0 vary b 1 0 vary c 0 5 Lower Bounds none Upper Bounds none Script Access langmuirext2 x a b c Function File FITFUNC LANGEXT2 FDF Last Updated 11 14 00 Page 131 of 166 Pareto Function 1 a y x Brief Description Pareto function Sample Curve yP A 1 0 1 0 Az 2 Y A Parameters Number 1 Names A Meanings A coefficient Initial Values A 1 0 vary Lower Bounds none Upper Bounds none Script Access pareto x A Function File FITFUNC PARETO FDF Last Updated 11 14 00 Page 132 of 166 Pow2P1 Function y all x Brief Description Two parameter power function Sample Curve Parameters Number 2 Names a b Meanings a coefficient b power Initial Values a 1 0 vary b 1 0 vary Lower Bounds none Upper Bounds none Script Access pow2p1 x a b Function File FITFUNC POW2P1 FDF Last Updated 11 14 00 Page 133 of 166 Pow2P2 Function y a 1 x Brief Description Two parameter power function
54. n Weibull peak function Sample Curve xc yO ia 9 y yO Parameters Number 5 Names yO xc A wl w2 Meanings y0 offset xc center A amplitude wl width w2 width Initial Values yO 0 0 vary xc 0 0 vary A 1 0 vary wl 1 0 vary w2 1 0 vary Lower Bounds wl gt 0 0 w2 gt 0 0 Upper Bounds none Script Access weibull3 x y0 xc A w1 w2 Function File FITFUNC WEIBULL3 FDF Last Updated 11 14 00 Page 112 of 166 8 Pharmacology Functions Biphasic DoseResp OneSiteBind OneSiteComp TwoSiteBind TwoSiteComp 114 115 116 117 118 119 Last Updated 11 14 00 Page 113 of 166 Biphasic Function 3E Araxi a A nin A 2 A nin A min 1 1079 091 E 1060 2 42 Brief Description Biphasic sigmoidal dose response 7 parameters logistic equation Sample Curve ATE Araxi Amin Arad Arin hih2 gt 0 batom Amin 0 yA irst and secondtop asymptotes Amaxi 2 f mmx 3 irst and secondtop medans x 1 1 x 2 8 sopeshi 02 h2 02 Parameters Number 7 Names Amin Amaxl Amax2 xO 1 xO 2 hl h2 Meanings Amin bottom asymptote Amax1 first top asymptote Amax2 second top asymptote xO 1 first median x0 2 second median h1 slope h2 slope Initial Values Amin 0 0 vary Amax1 1 0 vary Amax2 1 0 vary x0 1 1 0 vary x0 2 10 0 vary hl 1 0 vary h2 1 0 vary Lower Bounds none Upper Bounds none
55. nitial Values yO 0 0 vary xc 0 0 vary A 1 0 vary w 1 0 vary a3 1 0 vary a4 1 0 vary Lower Bounds A gt 0 0 w gt 0 0 Upper Bounds none Script Access ecs x y0 xc A w a3 a4 Function File FITFUNC EDGWTHCR FDF Last Updated 11 14 00 Page 25 of 166 Gauss Function A ME y 2 Y t me wNTI 2 Brief Description Area version of Gaussian function Sample Curve xc yc amp 0 offset yO 1 center xc 2 width w 1 5 area A 5 yczyO Aj w sqit pi 23 wewl fsqrt in 4 Parameters Number 4 Names y0 xc w A Meanings y0 offset xc center w width A area Initial Values yO 0 0 vary xc 0 0 vary w 1 0 vary A 10 vary Lower Bounds w gt 0 0 Upper Bounds none Script Access gauss x y0 xc w A Function File FITFUNC GAUSS FDF Last Updated 11 14 00 Page 26 of 166 GaussMod Function l w x x 2 A d oe do fo 2 t e J d e dy t oo 0 S c X X Ww where z Ww ty Brief Description Exponentially modified Gaussian peak function for use in chromatography Sample Curve offset y O armplitude A 1 center x width wel t 005 Ys Parameters Number 5 Names y0 A xc w tO Meanings y0 offset A amplitude xc center w width t0 unknown Initial Values yO 0 0 vary A 1 0 vary xc 0 0 vary w 1 0 vary t0 0 05 vary Lower Bounds w gt 0 0
56. ns Asymtoticl BoxLucas1 BoxLucasl Mod BoxLucas2 Chapman ExpIP1 Exp1P2 Exp1P2md Exp1P3 Exp1P3Md Exp1P4 Exp1P4Md Exp2P Exp2PMod1 Exp2PMod2 Exp3P1 Exp3P1Md Exp3P2 ExpAssoc ExpDecl ExpDec2 ExpDec3 ExpDecayl ExpDecay2 ExpDecay3 ExpGrol ExpGro2 ExpGro3 ExpGrowl ExpGrow2 ExpLinear Exponential MnMolecular MnMolecularl Shah Stirling YldFert YldFertl 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 Last Updated 11 14 00 Page 30 of 166 Asymptotic1 Function y a bc Brief Description Asymptotic regression model 1st parameterization Reference Ratkowksy David A 1990 Handbook of Nonlinear Regression Models Marcel Dekker Inc 4 3 1 Sample Curve asymptote a 1 response range b 1 rate c 0 5 Parameters Number 3 Names a b c Meanings a asymptote b response range c rate Initial Values a 1 0 vary b 1 0 vary c 0 5 Lower Bounds none Upper Bounds none Script Access Asymptotic1 x a b c Function File FITFUNC AS YMPT1 FDF Last Updated 11 14 00 Page 31 of 166 BoxLucas1 Function y all e Brief Description A parameterization of Box Lucas model Sample Curve Parameters Number 2 Names a b Meanings a coefficient b coefficient Initial Values a 1 0 vary b 1 0 vary Lower Bounds none Upper Bounds none Script Access boxlu
57. offset xO center Al amplitude t1 decay constant A2 amplitude t2 decay constant A3 amplitude t3 decay constant Initial Values yO 0 0 vary x0 0 0 vary Al 10 vary tl 1 0 vary A2 10 vary t2 1 0 vary A3 10 vary t3 1 0 vary Lower Bounds none Upper Bounds none Script Access expdecay3 x y0 x0 A 1 t1 A2 12 A3 13 Function File FITFUNC EXPDECY3 FDF Last Updated 11 14 00 Page 10 of 166 ExpGrow1 Function x xo t Y Yy t Aje Brief Description Exponential growth 1 with offset Sample Curve center x 1 amplitude A 2 idth t 1 Parameters Number 4 Names y0 x0 Al t1 Meanings y0 offset xO center Al amplitude t1 width Initial Values yO 0 0 vary x0 0 0 vary Al 1 0 vary t1 1 0 vary Lower Bounds t1 gt 0 0 Upper Bounds none Script Access expgrow1 x y0 x0 A1 t1 Function File FITFUNC EXPGROW1 FDF Last Updated 11 14 00 Page 11 of 166 ExpGrow2 Function yey y Aeon A eh Brief Description Exponential growth 2 with offset Sample Curve offset y0 0 center x g 0 amplitude A1 1 width t1 1 x0 yO A1 A2 amplitude A2 2 width t2 2 y y0 Parameters Number 6 Names y0 x0 A1 t1 A2 t2 vy DA 17 1 A 2 t2 Meanings y0 offset xO center Al amplitude t1 width A2 amplitude t2 width Initial Values yO 0 0 vary x0 0 0 vary Al 1 0 vary t1 1
58. rs Number 9 Names y0 xcl A w k2 xc2 B k3 xc3 Meanings y0 offset xcl unknown A unknown w unknown k2 unknown xc2 unknown B unknown k3 unknown xc3 unknown Initial Values yO 0 0 vary xcl 1 0 vary A 1 0 vary w 1 0 vary k2 1 0 vary xc2 1 0 vary B 1 0 vary k3 1 0 vary xc3 1 0 vary Lower Bounds w gt 0 0 Upper Bounds none Script Access cce x y0 xc1 A w k2 xc2 B k3 xc3 Function File FITFUNC CHESLECR FDF Last Updated 11 14 00 Page 96 of 166 ECS Function where z Brief Description Edgeworth Cramer peak function for use in chromatography Sample Curve Parameters Number 6 Names yO xc A w a3 a4 12 2 2 2 ient 62 3 3 10a offset y 1 center x 0 am plitude 4 5 width w 1 ar2 a2 2 15z e 452 15 Meanings y0 offset xc center A amplitude w width a3 unknown a4 unknown Initial Values yO 0 0 vary xc 0 0 vary A 1 0 vary w 1 0 vary a3 1 0 vary a4 1 0 vary Lower Bounds A gt 0 0 w gt 0 0 Upper Bounds none Script Access ecs x y0 xc A w a3 a4 Function File FITFUNC EDGWTHCR FDF Last Updated 11 14 00 Page 97 of 166 Extreme Function EE TEERY Brief Description Extreme function in statistics Sample Curve xc yO 4 y 0 w gt Q A20 offset y0 0 Center xc 1 Width w 1 Amplitude A 1 0
59. rve Parameters Number 3 Names a b c Meanings a offset b coefficient c power Initial Values a 1 0 vary b 1 0 vary c 0 5 vary Lower Bounds none Upper Bounds none Script Access allometric2 x a b c Function File FITFUNC ALLOMET2 FDF Last Updated 11 14 00 Page 122 of 166 Asym2Sig Function 1 1 y Yo T A x xo0w 2 x x w 2 l e l e Brief Description Asymmetric double sigmoidal Sample Curve A wl w2 w3 affset y 0 centerxc arrplitude A 1 widthw1 1 yy widthiw2 2 widthiw3 3 Parameters Number 6 Names yO xc A wl w2 w3 Meanings y0 offset xc center A amplitude wl width w2 width w3 width Initial Values yO 0 0 vary xc 0 0 vary A 1 0 vary w1 1 0 vary w2 1 0 vary w3 1 0 vary Lower Bounds wl gt 0 0 w2 gt 0 0 w3 gt 0 0 Upper Bounds none Script Access asym2sig x y0 xc A w1 w2 w3 Function File FITFUNC AS YMDBLS FDF Last Updated 11 14 00 Page 123 of 166 Belehradek Function y 2 a x b Brief Description Belehradek model Sample Curve a 1 a 1 a 1 position b 1 pos ition b 1 position b 1 powerc 2 power c 05 y7 0 y 0 Parameters Number 3 Names a b c Meanings a coefficient b position c power Initial Values a 1 0 vary b 1 0 vary c 0 5 Lower Bounds none Upper Bounds none Script Access belehradek x a b c
60. t Access expgro3 x y0 A 1 t1 A2 t2 A3 t3 Function File FITFUNC EXPGRO3 FDF Last Updated 11 14 00 Page 58 of 166 ExpGrow1 Function x xo t Y Yy t Aje Brief Description Exponential growth 1 with offset Sample Curve center x 1 amplitude A 2 idth t 1 Parameters Number 4 Names y0 x0 Al t1 Meanings y0 offset xO center Al amplitude t1 width Initial Values yO 0 0 vary x0 0 0 vary A1 1 0 vary t1 1 0 vary Lower Bounds tl gt 0 0 Upper Bounds none Script Access expgrow1 x y0 x0 A1 t1 Function File FITFUNC EXPGROW1 FDF Last Updated 11 14 00 Page 59 of 166 ExpGrow2 Function yey y Aeon A eh Brief Description Exponential growth 2 with offset Sample Curve offset y0 0 center x g 0 amplitude A1 1 width t1 1 x0 yO A1 A2 amplitude A2 2 width t2 2 y y0 Parameters Number 6 Names y0 x0 A1 t1 A2 t2 vy DA 17 1 A 2 t2 Meanings y0 offset xO center Al amplitude t1 width A2 amplitude t2 width Initial Values yO 0 0 vary x0 0 0 vary Al 1 0 vary t1 1 0 vary A2 1 0 vary t2 1 0 vary Lower Bounds t1 0 0 t2 0 0 Upper Bounds none Script Access expgrow2 x y0 x0 A1 11 A2 12 Function File FITFUNC EXPGROW2 FDF Last Updated 11 14 00 Page 60 of 166 ExpLinear Function yape pp tpat Brief Description Exponential linear combination Reference S
61. unction File FITFUNC GAUSSAMP FDF Last Updated 11 14 00 Page 156 of 166 InvsPoly Function A peg 2 4 6 afa Zo er 2 Ww Ww Ww Brief Description Inverse polynomial peak function with center Sample Curve R22D0D w l w2D 4 n AsO AZO AsO Aico RZ hAZ 34A1 A3 U yU D xce1 w 5 y U xce 1 5 A2 3 A1 A3 nD A10 AJ gt 0 Restated Asi Aisi yO 0 xcs 1 5 AZ 1 A3 1 AZe1 A3 41 A 1 A 1e1 AZ 3 A3 7 3 y y 0 yoo Parameters Number 7 Names y0 xc w A Al A2 A3 Meanings y0 offset xc center w width A amplitude Al coefficient A2 coefficient A3 coefficient Initial Values yO 0 0 vary xc 0 0 vary w 1 0 vary A 1 0 vary Al 0 0 vary A2 0 0 vary A3 0 0 vary Lower Bounds w gt 0 0 Al 2 0 0 A22 0 0 A32 0 0 Upper Bounds none Script Access invspoly x y0 xc w A A1 A2 A3 Function File FITFUNCUNVSPOLY FDF Last Updated 11 14 00 Page 157 of 166 Lorentz Function 2A w Y Yo T A x x w Brief Description Lorentzian peak function Sample Curve xc yc yS OHA w pi Parameters Number 4 Names y0 xc w A Meanings y0 offset xc center w width A area Initial Values y0 0 0 vary xc 0 0 vary w 1 0 vary A 1 0 vary Lower Bounds w gt 0 0 Upper Bounds none Script Access lorentz x y0 xc w A Function File FITFUNC LORENTZ FDF Last Updated 11 14 00 P
62. y b 1 0 vary k 1 0 vary Lower Bounds none Upper Bounds none Script Access stirling x a b k Function File FITFUNC STIRLING FDF Last Updated 11 14 00 Page 66 of 166 YidFert Function y a t br Brief Description Yield fertilizer model in agriculture and learning curve in psychology Sample Curve Parameters Number 3 Names a b r Meanings a offset b coefficient r coefficient Initial Values a 1 0 vary b 1 0 vary r 0 5 vary Lower Bounds r 0 0 Upper Bounds r 1 0 Script Access yldfert x a b r Function File FITFUNC YLDFERT FDF Last Updated 11 14 00 Page 67 of 166 YidFert1 Function y atbe Brief Description Yield fertilizer model in agriculture and learning curve in psychology Sample Curve of amp et a 5 b 1 k 05 D a b 0 a b ya ya Parameters Number 3 Names a b k Meanings a offset b coefficient k coefficient Initial Values a 1 0 vary b 1 0 vary k 0 5 vary Lower Bounds k 0 0 Upper Bounds none Script Access yldfert1 x a b k Function File FITFUNC YLDFERT1 FDF Last Updated 11 14 00 Page 68 of 166 4 Growth Sigmoidal Boltzmann Hill Logistic SGompertz SLogisticl SLogistic2 SLogistic3 SRichards1 SRichards2 SWeibulll SWeibull2 70 71 72 73 74 75 76 77 78 79 80 Last Updated 11 14 00 Page 69 of 166 Boltzmann Function __A A A Pc x x
63. y dx 2 l e Brief Description Boltzmann function produces a sigmoidal curve Sample Curve y A2 init value A120 final value A2 21 center x0 0 time constdx 1 x0 A1 A 23 2 y A 2 A 1 4 dx y A1 Parameters Number 4 Names Al A2 x0 dx Meanings A1 initial value A2 final value x0 center dx time constant Initial Values A1 0 0 vary A2 1 0 vary x0 0 0 vary dx 1 0 vary Lower Bounds none Upper Bounds none Constraints dx 0 Script Access boltzman x A1 A2 x0 dx Function File FITFUNC BOLTZMAN FDF Last Updated 11 14 00 Page 70 of 166 Hill Function n X Y Vs k x Brief Description Hill function Reference Seber G A F Wild C J 1989 Nonlinear Regression John Wiley amp Sons Inc p 120 Sample Curve yzV max x nz k n n 1 n 1 x0 y0 y 2 0 0 0 Parameters Number 3 Names Vmax k n Meanings Vmax unknown k unknown n unknown Initial Values Vmax 1 0 vary k 1 0 vary n 1 5 vary Lower Bounds Vmax gt 0 Upper Bounds none Script Access hill x Vmax k n Function File FITFUNC HILL FDF Last Updated 11 14 00 Page 71 of 166 Logistic Function A A M Haut NND d xy C Brief Description Logistic dose response in pharmacology chemistry Sample Curve init alue A1 0 final value A271 center x0 5 y A2 power p 3 x1 0 p p 1 p x1 y1
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