Curve Fitting Functions

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Last Updated 11/14/00 Page 1 of 166 Curve Fitting Functions Contents 1. ORIGIN BASIC FUNCTIONS .......................................................................................................................... 2 2. CHROMATOGRAPHY FUNCTIONS ............................................................................................................... 23 3. EXPONENTIAL FUNCTIONS ........................................................................................................................ 30 4. GROWTH/SIGMOIDAL ................................................................................................................................ 69 5. HYPERBOLA FUNCTIONS ........................................................................................................................... 81 6. LOGARITHM FUNCTIONS ........................................................................................................................... 87 7. PEAK FUNCTIONS ...................................................................................................................................... 93 8. PHARMACOLOGY FUNCTIONS.................................................................................................................. 113 9. POWER FUNCTIONS ................................................................................................................................. 120 10. RATIONAL FUNCTIONS .......................................................................................................................... 140 11. SPECTROSCOPY FUNCTIONS .................................................................................................................. 155 12. WAVEFORM FUNCTIONS........................................................................................................................ 163

Transcript of Curve Fitting Functions

Last Updated 11/14/00 Page 1 of 166Curve Fitting FunctionsContents1. ORIGIN BASIC FUNCTIONS .......................................................................................................................... 22. CHROMATOGRAPHY FUNCTIONS ............................................................................................................... 233. EXPONENTIAL FUNCTIONS ........................................................................................................................ 304. GROWTH/SIGMOIDAL................................................................................................................................ 695. HYPERBOLA FUNCTIONS ........................................................................................................................... 816. LOGARITHM FUNCTIONS ........................................................................................................................... 877. PEAK FUNCTIONS ...................................................................................................................................... 938. PHARMACOLOGY FUNCTIONS.................................................................................................................. 1139. POWER FUNCTIONS ................................................................................................................................. 12010. RATIONAL FUNCTIONS .......................................................................................................................... 14011. SPECTROSCOPY FUNCTIONS .................................................................................................................. 15512. WAVEFORM FUNCTIONS........................................................................................................................ 163Last Updated 11/14/00 Page 2 of 1661. Origin Basic FunctionsAllometric1 3Beta 4Boltzmann 5Dhyperbl 6ExpAssoc 7ExpDecay1 8ExpDecay2 9ExpDecay3 10ExpGrow1 11ExpGrow2 12Gauss 13GaussAmp 14Hyperbl 15Logistic 16LogNormal 17Lorentz 18Pulse 19Rational0 20Sine 21Voigt 22Last Updated 11/14/00 Page 3 of 166Allometric1Functionbax y Brief DescriptionClassical Freundlich model. Has been used in the study of allometry.Sample CurveParametersNumber: 2Names: a, bMeanings: a = coefficient, b = powerInitial Values: a = 1.0 (vary), b = 0.5 (vary)Lower Bounds: noneUpper Bounds: noneScript Accessallometric1(x,a,b)Function FileFITFUNC\ALLOMET1.FDFLast Updated 11/14/00 Page 4 of 166BetaFunction11 33 211 23 203 2121121 ]]]

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.| ++ + wcwcwx xww wwx xww wA y yBrief DescriptionThe beta function.Sample CurveParametersNumber: 6Names: y0, xc, A, w1, w2, w3Meanings: y0 = offset, xc = center, A = amplitude, w1 = width, w2 = width, w3 = widthInitial Values: y0 = 0.0 (vary), xc = 1.0 (vary), A = 5.0 (vary), w1 = 5.0 (vary), w2 = 2.0 (vary), w3 = 2.0(vary)Lower Bounds: w1 > 0.0, w2 > 1.0, w3 > 1.0Upper Bounds: noneScript Accessbeta(x,y0,xc,A,w1,w2,w3)Function FileFITFUNC\BETA.FDFLast Updated 11/14/00 Page 5 of 166BoltzmannFunction( ) 2 /2 101 AeA Aydx x x ++Brief DescriptionBoltzmann function - produces a sigmoidal curve.Sample CurveParametersNumber: 4Names: A1, A2, x0, dxMeanings: A1 = initial value, A2 = final value, x0 = center, dx = time constantInitial Values: A1 = 0.0 (vary), A2 = 1.0 (vary), x0 = 0.0 (vary), dx = 1.0 (vary)Lower Bounds: noneUpper Bounds: noneConstraintsdx ! = 0Script Accessboltzman(x,A1,A2,x0,dx)Function FileFITFUNC\BOLTZMAN.FDFLast Updated 11/14/00 Page 6 of 166DhyperblFunctionx Px Px Px Px Py54321++++Brief DescriptionDouble rectangular hyperbola function.Sample CurveParametersNumber: 5Names: P1, P2, P3, P4, P5Meanings: Unknowns 1-5Initial Values: P1 = 1.0 (vary), P2 = 1.0 (vary), P3 = 1.0 (vary), P4 = 1.0 (vary), P5 = 1.0 (vary)Lower Bounds: noneUpper Bounds: noneScript Accessdhyperbl(x,P1,P2,P3,P4,P5)Function FileFITFUNC\DHYPERBL.FDFLast Updated 11/14/00 Page 7 of 166ExpAssocFunction( ) ( )2 1/2/1 01 1 t x t xe A e A y y + + Brief DescriptionExponential associate.Sample CurveParametersNumber: 5Names: y0, A1, t1, A2, t2Meanings: y0 = offset, A1 = amplitude, t1 = width, A2 = amplitude, t2 = widthInitial Values: y0 = 0.0 (vary), A1 = 1.0 (vary), t1 = 1.0 (vary), A2 = 1.0 (vary), t2 = 1.0 (vary)Lower Bounds: t1 > 0, t2 > 0Upper Bounds: noneScript Accessexpassoc(x,y0,A1,t1,A2,t2)Function FileFITFUNC\EXPASSOC.FDFLast Updated 11/14/00 Page 8 of 166ExpDecay1Function( )1 0/1 0t x xe A y y + Brief DescriptionExponential decay 1 with offset.Sample CurveParametersNumber: 4Names: y0, x0, A1, t1Meanings: y0 = offset, x0 = center, A1 = amplitude, t1 = decay constantInitial Values: y0 = 0.0 (vary), x0 = 0.0 (vary), A1 = 10 (vary), t1 = 1.0 (vary)Lower Bounds: noneUpper Bounds: noneScript Accessexpdecay1(x,y0,x0,A1,t1)Function FileFITFUNC\EXPDECY1.FDFLast Updated 11/14/00 Page 9 of 166ExpDecay2Function( ) ( )2 0 1 0/2/1 0t x x t x xe A e A y y + + Brief DescriptionExponential decay 2 with offset.Sample CurveParametersNumber: 6Names: y0, x0, A1, t1, A2, t2Meanings: y0 = offset, x0 = center, A1 = amplitude, t1 = decay constant, A2 = amplitude, t2 = decayconstantInitial Values: y0 = 0.0 (vary), x0 = 0.0 (vary), A1 = 10 (vary), t1 = 1.0 (vary), A2 = 10 (vary), t2 = 1.0(vary)Lower Bounds: noneUpper Bounds: noneScript Accessexpdecay2(x,y0,x0,A1,t1,A2,t2)Function FileFITFUNC\EXPDECY2.FDFLast Updated 11/14/00 Page 10 of 166ExpDecay3Function( ) ( ) ( )3 0 2 0 1 0/3/2/1 0t x x t x x t x xe A e A e A y y + + + Brief DescriptionExponential decay 3 with offset.Sample CurveParametersNumber: 8Names: y0, x0, A1, t1, A2, t2, A3, t3Meanings: y0 = offset, x0 = center, A1 = amplitude, t1 = decay constant, A2 = amplitude, t2 = decayconstant, A3 = amplitude, t3 = decay constantInitial Values: y0 = 0.0 (vary), x0 = 0.0 (vary), A1 = 10 (vary), t1 = 1.0 (vary), A2 = 10 (vary), t2 = 1.0(vary), A3 = 10 (vary), t3 = 1.0 (vary)Lower Bounds: noneUpper Bounds: noneScript Accessexpdecay3(x,y0,x0,A1,t1,A2,t2,A3,t3)Function FileFITFUNC\EXPDECY3.FDFLast Updated 11/14/00 Page 11 of 166ExpGrow1Function( )1 0/1 0t x xe A y y + Brief DescriptionExponential growth 1 with offset.Sample CurveParametersNumber: 4Names: y0, x0, A1, t1Meanings: y0 = offset, x0 = center, A1 = amplitude, t1 = widthInitial Values: y0 = 0.0 (vary), x0 = 0.0 (vary), A1 = 1.0 (vary), t1 = 1.0 (vary)Lower Bounds: t1 > 0.0Upper Bounds: noneScript Accessexpgrow1(x,y0,x0,A1,t1)Function FileFITFUNC\EXPGROW1.FDFLast Updated 11/14/00 Page 12 of 166ExpGrow2Function( ) ( )2 0 1 0/2/1 0t x x t x xe A e A y y + + Brief DescriptionExponential growth 2 with offset.Sample CurveParametersNumber: 6Names: y0, x0, A1, t1, A2, t2Meanings: y0 = offset, x0 = center, A1 = amplitude, t1 = width, A2 = amplitude, t2 = widthInitial Values: y0 = 0.0 (vary), x0 = 0.0 (vary), A1 = 1.0 (vary), t1 = 1.0 (vary), A2 = 1.0 (vary), t2 = 1.0(vary)Lower Bounds: t1 > 0.0, t2 > 0.0Upper Bounds: noneScript Accessexpgrow2(x,y0,x0,A1,t1,A2,t2)Function FileFITFUNC\EXPGROW2.FDFLast Updated 11/14/00 Page 13 of 166GaussFunction( )22202 /wx x cewAy y+ Brief DescriptionArea version of Gaussian function.Sample CurveParametersNumber: 4Names: y0, xc, w, AMeanings: y0 = offset, xc = center, w = width, A = areaInitial Values: y0 = 0.0 (vary), xc = 0.0 (vary), w = 1.0 (vary), A = 10 (vary)Lower Bounds: w > 0.0Upper Bounds: noneScript Accessgauss(x,y0,xc,w,A)Function FileFITFUNC\GAUSS.FDFLast Updated 11/14/00 Page 14 of 166GaussAmpFunction( )2220wx x cAe y y+ Brief DescriptionAmplitude version of Gaussian peak function.Sample CurveParametersNumber: 4Names: y0, xc, w, AMeanings: y0 = offset, xc = center, w = width, A = areaInitial Values: y0 = 0.0 (vary), xc = 0.0 (vary), w = 1.0 (vary), A = 10 (vary)Lower Bounds: w > 0.0Upper Bounds: noneScript Accessgaussamp(x,y0,xc,w,A)Function FileFITFUNC\GAUSSAMP.FDFLast Updated 11/14/00 Page 15 of 166HyperblFunctionx Px Py+21Brief DescriptionHyperbola function. Also the Michaelis-Menten model in enzyme kinetics.Sample CurveParametersNumber: 2Names: P1, P2Meanings: P1 = amplitude, P2 = unknownInitial Values: P1 = 1.0 (vary), P2 = 1.0 (vary)Lower Bounds: noneUpper Bounds: noneScript Accesshyperbl(x,P1,P2)Function FileFITFUNC\HYPERBL.FDFLast Updated 11/14/00 Page 16 of 166LogisticFunction( )202 1/ 1 Ax xA Ayp ++Brief DescriptionLogistic dose response in pharmacology/chemistry.Sample CurveParametersNumber: 4Names: A1, A2, x0, pMeanings: A1 = initial value, A2 = final value, x0 = center, p = powerInitial Values: A1 = 0.0 (vary), A2 = 1.0 (vary), x0 = 1.0 (vary), p = 1.5 (vary)Lower Bounds: p > 0.0Upper Bounds: noneScript Accesslogistic(x,A1,A2,x0,p)Function FileFITFUNC\LOGISTIC.FDFLast Updated 11/14/00 Page 17 of 166LogNormalFunction[ ]222/ ln02wx x cewxAy y+ Brief DescriptionLog-Normal function.Sample CurveParametersNumber: 4Names: y0, xc, w, AMeanings: y0 = offset, xc = center, w = width, A = amplitudeInitial Values: y0 = 0.0 (vary), xc = 1.0 (vary), w = 1.0 (vary), A = 1.0 (vary)Lower Bounds: xc > 0, w > 0Upper Bounds: noneScript Accesslognormal(x,y0,xc,w,A)Function FileFITFUNC\LOGNORM.FDFLast Updated 11/14/00 Page 18 of 166LorentzFunction( )2 2 042w x xw Ay yc + + Brief DescriptionLorentzian peak function.Sample CurveParametersNumber: 4Names: y0, xc, w, AMeanings: y0 = offset, xc = center, w = width, A = areaInitial Values: y0 = 0.0 (vary), xc = 0.0 (vary),w = 1.0 (vary), A = 1.0 (vary)Lower Bounds: w > 0.0Upper Bounds: noneScript Accesslorentz(x,y0,xc,w,A)Function FileFITFUNC\LORENTZ.FDFLast Updated 11/14/00 Page 19 of 166PulseFunction201010tx xptx xe e A y y

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.| + Brief DescriptionPulse function.Sample CurveParametersNumber: 6Names: y0, x0, A, t1, P, t2Meanings: y0 = offset, x0 = center, A = amplitude, t1 = width, P = power, t2 = widthInitial 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 > 0.0, t1 > 0.0, P > 0.0, t2 > 0.0Upper Bounds: noneScript Accesspulse(x,y0,x0,A,t1,P,t2)Function FileFITFUNC/PULSE.FDFLast Updated 11/14/00 Page 20 of 166Rational0Functionaxcx by++1Brief DescriptionRational function, type 0.Reference: Ratkowksy, David A. 1990. Handbook of Nonlinear Regression Models. Marcel Dekker, Inc.4.3.24Sample CurveParametersNumber: 3Names: a, b, cMeanings: a = coefficient, b = coefficient, c = coefficientInitial Values: a = 1.0 (vary), b = 1.0 (vary), c = 0.5Lower Bounds: noneUpper Bounds: noneScript Accessrational0(x,a,b,c)Function FileFITFUNC\RATION0.FDFLast Updated 11/14/00 Page 21 of 166SineFunction

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.| wx xA y c sinBrief DescriptionSine function.Sample CurveParametersNumber: 3Names: xc, w, AMeanings: xc = center, w = width, A = amplitudeInitial Values: xc = 0.0 (vary), w = 1.0 (vary), A = 1.0 (vary)Lower Bounds: w > 0.0Upper Bounds: noneScript Accesssine(x,xc,w,A)Function FileFITFUNC\SINE.FDFLast Updated 11/14/00 Page 22 of 166VoigtFunction

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.| + dttwx xwwewwA y yGcGLtGL2 2 2 2 / 3 02 ln 4 2 ln2 ln 22Brief DescriptionVoigt peak function.Sample CurveParametersNumber: 5Names: y0, xc, A, wG, wLMeanings: y0 = offset, xc = center, A = amplitude, wG = Gaussian width, wL = Lorentzian widthInitial Values: y0 = 0.0 (vary), xc = 0.0 (vary), A = 1.0 (vary), wG = 1.0 (vary), wL = 1.0 (vary)Lower Bounds: wG > 0.0, wL > 0.0Upper Bounds: noneScript Accessvoigt5(x,y0,xc,A,wG,wL)Function FileFITFUNC\VOIGT5.FDFLast Updated 11/14/00 Page 23 of 1662. Chromatography FunctionsCCE 24ECS 25Gauss 26GaussMod 27GCAS 28Giddings 29Last Updated 11/14/00 Page 24 of 166CCEFunction( )( ) ( ) ( ) ( ) ( ) ( )]]]]

+ + + 3 3 3215 . 0220tanh 1 5 . 0 1 c ccx x x x kcwx xe x x k B e A y yBrief DescriptionChesler-Cram peak function for use in chromatography.Sample CurveParametersNumber: 9Names: y0, xc1, A, w, k2, xc2, B, k3, xc3Meanings: y0 = offset, xc1 = unknown, A = unknown, w = unknown, k2 = unknown, xc2 = unknown, B =unknown, k3 = unknown, xc3 = unknownInitial Values: y0 = 0.0 (vary), xc1 = 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 > 0.0Upper Bounds: noneScript Accesscce(x,y0,xc1,A,w,k2,xc2,B,k3,xc3)Function FileFITFUNC\CHESLECR.FDFLast Updated 11/14/00 Page 25 of 166ECSFunction( ) ( )( )''

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.| + ++ + ++ 15 45 15! 6103 6! 43! 3122 4 6233 4 4 2 35 . 002z z zaz zaz zaewAy y zwhere wx xz cBrief DescriptionEdgeworth-Cramer peak function for use in chromatography.Sample CurveParametersNumber: 6Names: y0, xc, A, w, a3, a4Meanings: y0 = offset, xc = center, A = amplitude, w = width, a3 = unknown, a4 = unknownInitial Values: y0 = 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 > 0.0, w > 0.0Upper Bounds: noneScript Accessecs(x,y0,xc,A,w,a3,a4)Function FileFITFUNC\EDGWTHCR.FDFLast Updated 11/14/00 Page 26 of 166GaussFunction( )22202 /wx x cewAy y+ Brief DescriptionArea version of Gaussian function.Sample CurveParametersNumber: 4Names: y0, xc, w, AMeanings: y0 = offset, xc = center, w = width, A = areaInitial Values: y0 = 0.0 (vary), xc = 0.0 (vary), w = 1.0 (vary), A = 10 (vary)Lower Bounds: w > 0.0Upper Bounds: noneScript Accessgauss(x,y0,xc,w,A)Function FileFITFUNC\GAUSS.FDFLast Updated 11/14/00 Page 27 of 166GaussModFunction

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.|+ z ytx xtwdy e etAy x fc22100202021) (where 0twwx xz cBrief DescriptionExponentially modified Gaussian peak function for use in chromatography.Sample CurveParametersNumber: 5Names: y0, A, xc, w, t0Meanings: y0 = offset, A = amplitude, xc = center, w = width, t0 = unknownInitial Values: y0 = 0.0 (vary), A = 1.0 (vary), xc = 0.0 (vary), w = 1.0 (vary), t0 = 0.05 (vary)Lower Bounds: w > 0.0, t0 > 0.0Upper Bounds: noneScript Accessgaussmod(x,y0,A,xc,w,t0)Function FileFITFUNC\GAUSSMOD.FDFLast Updated 11/14/00 Page 28 of 166GCASFunction( ),`

.|+ + z HiaewAy z f iii z432 /0!12) (23 633 4433+ z z Hz z Hwx xz cBrief DescriptionGram-Charlier peak function for use in chromatography.Sample CurveParametersNumber: 6Names: y0, xc, A, w, a3, a4Meanings: y0 = offset, xc = center, A = amplitude, w = width, a3 = unknown, a4 = unknownInitial Values: y0 = 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 > 0.0Upper Bounds: noneScript Accessgcas(x,y0,xc,A,w,a3,a4)Function FileFITFUNC\GRMCHARL.FDFLast Updated 11/14/00 Page 29 of 166GiddingsFunctionwx xc ccewx xIxxwAy y

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.|+ 21 0Brief DescriptionGiddings peak function for use in chromatography.Sample CurveParametersNumber: 4Names: y0, xc, w, AMeanings: y0 = offset, xc = center, w = width, A = areaInitial Values: y0 = 0.0 (vary), xc = 1.0 (vary), w = 1.0 (vary), A = 1.0 (vary)Lower Bounds: w > 0.0Upper Bounds: noneScript Accessgiddings(x,y0,xc,w,A)Function FileFITFUNC\GIDDINGS.FDFLast Updated 11/14/00 Page 30 of 1663. Exponential FunctionsAsymtotic1 31BoxLucas1 32BoxLucas1Mod 33BoxLucas2 34Chapman 35Exp1P1 36Exp1P2 37Exp1P2md 38Exp1P3 39Exp1P3Md 40Exp1P4 41Exp1P4Md 42Exp2P 43Exp2PMod1 44Exp2PMod2 45Exp3P1 46Exp3P1Md 47Exp3P2 48ExpAssoc 49ExpDec1 50ExpDec2 51ExpDec3 52ExpDecay1 53ExpDecay2 54ExpDecay3 55ExpGro1 56ExpGro2 57ExpGro3 58ExpGrow1 59ExpGrow2 60ExpLinear 61Exponential 62MnMolecular 63MnMolecular1 64Shah 65Stirling 66YldFert 67YldFert1 68Last Updated 11/14/00 Page 31 of 166Asymptotic1Functionxbc a y Brief DescriptionAsymptotic regression model - 1st parameterization.Reference: Ratkowksy, David A. 1990. Handbook of Nonlinear Regression Models. Marcel Dekker, Inc.4.3.1Sample CurveParametersNumber: 3Names: a, b, cMeanings: a = asymptote, b = response range, c = rateInitial Values: a = 1.0 (vary), b = 1.0 (vary), c = 0.5Lower Bounds: noneUpper Bounds: noneScript AccessAsymptotic1(x,a,b,c)Function FileFITFUNC\ASYMPT1.FDFLast Updated 11/14/00 Page 32 of 166BoxLucas1Function( )bxe a y 1Brief DescriptionA parameterization of Box Lucas model.Sample CurveParametersNumber: 2Names: a, bMeanings: a = coefficient, b = coefficientInitial Values: a = 1.0 (vary), b = 1.0 (vary)Lower Bounds: noneUpper Bounds: noneScript Accessboxlucas1(x,a,b)Function FileFITFUNC\BOXLUC1.FDFLast Updated 11/14/00 Page 33 of 166BoxLucas1ModFunction( )xb a y 1Brief DescriptionA parameterization of Box Lucas model.Reference: Ratkowksy, David A. 1990. Handbook of Nonlinear Regression Models. Marcel Dekker, Inc.4.3.5Sample CurveParametersNumber: 2Names: a, bMeanings: a = coefficient, b = coefficientInitial Values: a = 1.0 (vary), b = 1.0 (vary)Lower Bounds: noneUpper Bounds: noneScript Accessboxlucas1mod(x,a,b)Function FileFITFUNC\BOXLC1MD.FDFLast Updated 11/14/00 Page 34 of 166BoxLucas2Function( )x a x ae ea aay1 22 11 Brief DescriptionA parameterization of Box Lucas model.Reference: Seber, G. A. F., Wild, C. J. 1989. Nonlinear Regression. John Wiley & Sons, Inc. p. 254Sample CurveParametersNumber: 2Names: a1, a2Meanings: a1 = unknown, a2 = unknownInitial Values: a1 = 2.0 (vary), a2 = 1.0 (vary)Lower Bounds: noneUpper Bounds: noneScript Accessboxlucas2(x,a1,a2)Function FileFITFUNC\BOXLUC2.FDFLast Updated 11/14/00 Page 35 of 166ChapmanFunction( )cbxe a y 1Brief DescriptionChapman model.Reference: Ratkowksy, David A. 1990. Handbook of Nonlinear Regression Models. Marcel Dekker, Inc.4.3.35Sample CurveParametersNumber: 3Names: a, b, cMeanings: a = coefficient, b = coefficient, c = coefficientInitial Values: a = 1.0 (vary), b = 1.0 (vary), c = 0.5Lower Bounds: noneUpper Bounds: noneScript Accesschapman(x,a,b,c)Function FileFITFUNC\CHAPMAN.FDFLast Updated 11/14/00 Page 36 of 166Exp1P1FunctionA xe y Brief DescriptionOne-parameter exponential function.Reference: Ratkowksy, David A. 1990. Handbook of Nonlinear Regression Models. Marcel Dekker, Inc.4.1.5Sample Curveposition:A=1 y(1)=1(A,1)y=0ParametersNumber: 1Names: AMeanings: A = positionInitial Values: A = 1.0 (vary)Lower Bounds: noneUpper Bounds: noneScript Accessexp1p1(x,A)Function FileFITFUNC\EXP1P1.FDFLast Updated 11/14/00 Page 37 of 166Exp1p2FunctionAxe y Brief DescriptionOne-parameter exponential function.Reference: Ratkowksy, David A. 1990. Handbook of Nonlinear Regression Models. Marcel Dekker, Inc.4.1.15Sample CurveParametersNumber: 1Names: AMeanings: A = coefficientInitial Values: A = 1.0 (vary)Lower Bounds: noneUpper Bounds: noneScript Accessexp1p2(x,A)Function FileFITFUNC\EXP1P2.FDFLast Updated 11/14/00 Page 38 of 166Exp1p2mdFunctionxB y Brief DescriptionOne-parameter exponential function.Reference: Ratkowksy, David A. 1990. Handbook of Nonlinear Regression Models. Marcel Dekker, Inc.4.1.16Sample CurveParametersNumber: 1Names: BMeanings: B = positionInitial Values: B = 1.0 (vary)Lower Bounds: noneUpper Bounds: noneScript Accessexp1p2md(x,B)Function FileFITFUNC\EXP1P2MD.FDFLast Updated 11/14/00 Page 39 of 166Exp1p3FunctionAxAe y Brief DescriptionOne-parameter exponential function.Reference: Ratkowksy, David A. 1990. Handbook of Nonlinear Regression Models. Marcel Dekker, Inc.4.1.13Sample CurveParametersNumber: 1Names: AMeanings: A = coefficientInitial Values: A = 1.0 (vary)Lower Bounds: noneUpper Bounds: noneScript Accessexp1p3(x,A)Function FileFITFUNC\EXP1P3.FDFLast Updated 11/14/00 Page 40 of 166Exp1P3MdFunction( ) xB B y ln Brief DescriptionOne-parameter exponential function.Reference: Ratkowksy, David A. 1990. Handbook of Nonlinear Regression Models. Marcel Dekker, Inc.4.1.14Sample CurveParametersNumber: 1Names: BMeanings: B = coefficientInitial Values: B = 5.0 (vary)Lower Bounds: noneUpper Bounds: noneScript Accessexp1p3md(x,B)Function FileFITFUNC\EXP1P3MD.DFDLast Updated 11/14/00 Page 41 of 166Exp1P4FunctionAxe y 1Brief DescriptionOne-parameter exponential function.Reference: Ratkowksy, David A. 1990. Handbook of Nonlinear Regression Models. Marcel Dekker, Inc.4.1.18Sample CurveParametersNumber: 1Names: AMeanings: A = coefficientInitial Values: A = 1.0 (vary)Lower Bounds: noneUpper Bounds: noneScript Accessexp1p4(x,A)Function FileFITFUNC\EXP1P4.FDFLast Updated 11/14/00 Page 42 of 166Exp1P4MdFunctionxB y 1Brief DescriptionOne-parameter exponential function.Reference: Ratkowksy, David A. 1990. Handbook of Nonlinear Regression Models. Marcel Dekker, Inc.4.1.19Sample CurveParametersNumber: 1Names: BMeanings: B = coefficientInitial Values: B = 1.0 (vary)Lower Bounds: noneUpper Bounds: noneScript Accessexp1p4md(x,B)Function FileFITFUNC\EXP1P4.FDFLast Updated 11/14/00 Page 43 of 166Exp2PFunctionxab y Brief DescriptionTwo-parameter exponential function.Reference: Ratkowksy, David A. 1990. Handbook of Nonlinear Regression Models. Marcel Dekker, Inc.4.2.9Sample CurveParametersNumber: 2Names: a, bMeanings: a = position, b = positionInitial Values: a = 1.0 (vary), b = 1.5 (vary)Lower Bounds: noneUpper Bounds: noneScript Accessexp2p(x,a,b)Function FileFITFUNC\EXP2P.FDFLast Updated 11/14/00 Page 44 of 166Exp2PMod1Functionbxae y Brief DescriptionTwo-parameter exponential function.Reference: Ratkowksy, David A. 1990. Handbook of Nonlinear Regression Models. Marcel Dekker, Inc.4.2.10Sample CurveParametersNumber: 2Names: a, bMeanings: a = coefficient, b = rateInitial Values: a = 1.0 (vary), b = 1.5 (vary)Lower Bounds: noneUpper Bounds: noneScript Accessexp2pmod1(x,a,b)Function FileFITFUNC\EXP2PMD1.FDFLast Updated 11/14/00 Page 45 of 166Exp2PMod2Functionbx ae y +Brief DescriptionTwo-parameter exponential function.Reference: Ratkowksy, David A. 1990. Handbook of Nonlinear Regression Models. Marcel Dekker, Inc.4.2.11Sample CurveParametersNumber: 2Names: a, bMeanings: a = coefficient, b = rateInitial Values: a = 1.0 (vary), b =1.5 (vary)Lower Bounds: noneUpper Bounds: noneScript Accessexp2pmod2(x,a,b)Function FileFITFUNC\EXP2PMD2.FDFLast Updated 11/14/00 Page 46 of 166Exp3P1Functionc xbae y +Brief DescriptionThree-parameter exponential function.Reference: Ratkowksy, David A. 1990. Handbook of Nonlinear Regression Models. Marcel Dekker, Inc.4.3.33Sample CurveParametersNumber: 3Names: a, b, cMeanings: a = coefficient, b = coefficient, c = coefficientInitial Values: a = 1.0 (vary), b = 1.0 (vary), c = 0.5Lower Bounds: noneUpper Bounds: noneScript Accessexp3p1(x,a,b,c)Function FileFITFUNC\EXP3P1.FDFLast Updated 11/14/00 Page 47 of 166Exp3P1MdFunctionc xbae y ++Brief DescriptionThree-parameter exponential function.Reference: Ratkowksy, David A. 1990. Handbook of Nonlinear Regression Models. Marcel Dekker, Inc.4.3.34Sample CurveParametersNumber: 3Names: a, b, cMeanings: a = coefficient, b = coefficient, c = coefficientInitial Values: a = 1.0 (vary), b = 1.0 (vary), c = 0.5Lower Bounds: noneUpper Bounds: noneScript Accessexp3p1md(x,a,b,c)Function FileFITFUNC\EXP3P1MD.FDFLast Updated 11/14/00 Page 48 of 166Exp3P2Function2cx bx ae y + +Brief DescriptionThree-parameter exponential function.Reference: Ratkowksy, David A. 1990. Handbook of Nonlinear Regression Models. Marcel Dekker, Inc.4.3.39Sample CurveParametersNumber: 3Names: a, b, cMeanings: a = coefficient, b = coefficient, c = coefficientInitial Values: a = 1.0 (vary), b = 1.0 (vary), c = 0.5Lower Bounds: noneUpper Bounds: noneScript Accessexp3p2(x,a,b,c)Function FileFITFUNC\EXP3P2.FDFLast Updated 11/14/00 Page 49 of 166ExpAssocFunction( ) ( )2 1/2/1 01 1 t x t xe A e A y y + + Brief DescriptionExponential associate.Sample CurveParametersNumber: 5Names: y0, A1, t1, A2, t2Meanings: y0 = offset, A1 = amplitude, t1 = width, A2 = amplitude, t2 = widthInitial Values: y0 = 0.0 (vary), A1 = 1.0 (vary), t1 = 1.0 (vary), A2 = 1.0 (vary), t2 = 1.0 (vary)Lower Bounds: t1 > 0, t2 > 0Upper Bounds: noneScript Accessexpassoc(x,y0,A1,t1,A2,t2)Function FileFITFUNC\EXPASSOC.FDFLast Updated 11/14/00 Page 50 of 166ExpDec1Functiont xAe y y/0+ Brief DescriptionExponential decay 1.Sample CurveParametersNumber: 3Names: y0, A, tMeanings: y0 = offset, A = amplitude, t = decay constantInitial Values: y0 = 0.0 (vary), A = 1.0 (vary), t = 1.0 (vary)Lower Bounds: noneUpper Bounds: noneScript Accessexpdec1(x,y0,A,t)Function FileFITFUNC\EXPDEC1.FDFLast Updated 11/14/00 Page 51 of 166ExpDec2Function2 1/2/1 0t x t xe A e A y y + + Brief DescriptionExponential decay 2.Sample CurveParametersNumber: 5Names: y0, A1, t1, A2, t2Meanings: y0 = offset, A1 = amplitude, t1 = decay constant, A2 = amplitude, t2 = decay constantInitial Values: y0 = 0.0 (vary), A1 = 1.0 (vary), t1 = 1.0 (vary), A2 = 1.0 (vary), t2 = 1.0 (vary)Lower Bounds: noneUpper Bounds: noneScript Accessexpdec2(x,y0,A1,t1,A2,t2)Function FileFITFUNC\EXPDEC2.FDFLast Updated 11/14/00 Page 52 of 166ExpDec3Function3 2 1/3/2/1 0t x t x t xe A e A e A y y + + + Brief DescriptionExponential decay 3.Sample CurveParametersNumber: 7Names: y0, A1, t1, A2, t2, A3, t3Meanings: y0 = offset, A1 = amplitude, t1 = decay constant, A2 = amplitude, t2 = decay constant, A3 =amplitude, t3 = decay constantInitial Values: y0 = 0.0 (vary), A1 = 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: noneUpper Bounds: noneScript Accessexpdec3(x,y0,A1,t1,A2,t2,A3,t3)Function FileFITFUNC\EXPDEC3.FDFLast Updated 11/14/00 Page 53 of 166ExpDecay1Function( )1 0/1 0t x xe A y y + Brief DescriptionExponential decay 1 with offset.Sample CurveParametersNumber: 4Names: y0, x0, A1, t1Meanings: y0 = offset, x0 = center, A1 = amplitude, t1 = decay constantInitial Values: y0 = 0.0 (vary), x0 = 0.0 (vary), A1 = 10 (vary), t1 = 1.0 (vary)Lower Bounds: noneUpper Bounds: noneScript Accessexpdecay1(x,y0,x0,A1,t1)Function FileFITFUNC\EXPDECY1.FDFLast Updated 11/14/00 Page 54 of 166ExpDecay2Function( ) ( )2 0 1 0/2/1 0t x x t x xe A e A y y + + Brief DescriptionExponential decay 2 with offset.Sample CurveParametersNumber: 6Names: y0, x0, A1, t1, A2, t2Meanings: y0 = offset, x0 = center, A1 = amplitude, t1 = decay constant, A2 = amplitude, t2 = decayconstantInitial Values: y0 = 0.0 (vary), x0 = 0.0 (vary), A1 = 10 (vary), t1 = 1.0 (vary), A2 = 10 (vary), t2 = 1.0(vary)Lower Bounds: noneUpper Bounds: noneScript Accessexpdecay2(x,y0,x0,A1,t1,A2,t2)Function FileFITFUNC\EXPDECY2.FDFLast Updated 11/14/00 Page 55 of 166ExpDecay3Function( ) ( ) ( )3 0 2 0 1 0/3/2/1 0t x x t x x t x xe A e A e A y y + + + Brief DescriptionExponential decay 3 with offset.Sample CurveParametersNumber: 8Names: y0, x0, A1, t1, A2, t2, A3, t3Meanings: y0 = offset, x0 = center, A1 = amplitude, t1 = decay constant, A2 = amplitude, t2 = decayconstant, A3 = amplitude, t3 = decay constantInitial Values: y0 = 0.0 (vary), x0 = 0.0 (vary), A1 = 10 (vary), t1 = 1.0 (vary), A2 = 10 (vary), t2 = 1.0(vary), A3 = 10 (vary), t3 = 1.0 (vary)Lower Bounds: noneUpper Bounds: noneScript Accessexpdecay3(x,y0,x0,A1,t1,A2,t2,A3,t3)Function FileFITFUNC\EXPDECY3.FDFLast Updated 11/14/00 Page 56 of 166ExpGro1Function1/1 0t xe A y y + Brief DescriptionExponential growth 1.Sample CurveParametersNumber: 3Names: y0, A1, t1Meanings: y0 = offset, A1 = amplitude, t1 = growth constantInitial Values: y0 = 0.0 (vary), A1 = 1.0 (vary), t1 = 1.0 (vary)Lower Bounds: noneUpper Bounds: noneScript Accessexpgro1(x,y0,A1,t1)Function FileFITFUNC\EXPGRO1.FDFLast Updated 11/14/00 Page 57 of 166ExpGro2Function2 1/2/1 0t x t xe A e A y y + + Brief DescriptionExponential growth 2.Sample CurveParametersNumber: 5Names: y0, A1, t1, A2, t2Meanings: y0 = offset, A1 = amplitude, t1 = growth constant, A2 = amplitude, t2 = growth constantInitial Values: y0 = 0.0 (vary), A1 = 1.0 (vary), t1 = 1.0 (vary), A2 = 1.0 (vary), t2 = 1.0 (vary)Lower Bounds: noneUpper Bounds: noneScript Accessexpgro2(x,y0,A1,t1,A2,t2)Function FileFITFUNC\EXPGRO2.FDFLast Updated 11/14/00 Page 58 of 166ExpGro3Function3 2 1/3/2/1 0t x t x t xe A e A e A y y + + + Brief DescriptionExponential growth 3.Sample CurveParametersNumber: 7Names: y0, A1, t1, A2, t2, A3, t3Meanings: y0 = offset, A1 = amplitude, t1 = growth constant, A2 = amplitude, t2 = growth constant, A3 =amplitude, t3 = growth constantInitial Values: y0 = 0.0 (vary), A1 = 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: noneUpper Bounds: noneScript Accessexpgro3(x,y0,A1,t1,A2,t2,A3,t3)Function FileFITFUNC\EXPGRO3.FDFLast Updated 11/14/00 Page 59 of 166ExpGrow1Function( )1 0/1 0t x xe A y y + Brief DescriptionExponential growth 1 with offset.Sample CurveParametersNumber: 4Names: y0, x0, A1, t1Meanings: y0 = offset, x0 = center, A1 = amplitude, t1 = widthInitial Values: y0 = 0.0 (vary), x0 = 0.0 (vary),A1 = 1.0 (vary), t1 = 1.0 (vary)Lower Bounds: t1 > 0.0Upper Bounds: noneScript Accessexpgrow1(x,y0,x0,A1,t1)Function FileFITFUNC\EXPGROW1.FDFLast Updated 11/14/00 Page 60 of 166ExpGrow2Function( ) ( )2 0 1 0/2/1 0t x x t x xe A e A y y + + Brief DescriptionExponential growth 2 with offset.Sample CurveParametersNumber: 6Names: y0, x0, A1, t1, A2, t2Meanings: y0 = offset, x0 = center, A1 = amplitude, t1 = width, A2 = amplitude, t2 = widthInitial Values: y0 = 0.0 (vary), x0 = 0.0 (vary), A1 = 1.0 (vary), t1 = 1.0 (vary), A2 = 1.0 (vary), t2 = 1.0(vary)Lower Bounds: t1 > 0.0, t2 > 0.0Upper Bounds: noneScript Accessexpgrow2(x,y0,x0,A1,t1,A2,t2)Function FileFITFUNC\EXPGROW2.FDFLast Updated 11/14/00 Page 61 of 166ExpLinearFunctionx p p e p y p x4 3/12+ + Brief DescriptionExponential linear combination.Reference: Seber, G. A. F., Wild, C. J. 1989. Nonlinear Regression. John Wiley & Sons, Inc. p. 298Sample CurveParametersNumber: 4Names: p1, p2, p3, p4Meanings: p1 = coefficient, p2 = unknown, p3 = offset, p4 = coefficientInitial Values: p1 = 1.0 (vary), p2 = 1.0 (vary), p3 = 1.0 (vary), p4 = 1.0 (vary)Lower Bounds: noneUpper Bounds: noneScript Accessexplinear(x,p1,p2,p3,p4)Function FileFITFUNC\EXPLINEA.FDFLast Updated 11/14/00 Page 62 of 166ExponentialFunctionx RAe y y00 + Brief DescriptionExponential.Sample CurveParametersNumber: 3Names: y0, A, R0Meanings: y0 = offset, A = initial value, R0 = rateInitial Values: y0 = 0.0 (vary), A = 1.0 (vary), R0 = 1.0 (vary)Lower Bounds: A > 0.0Upper Bounds: noneScript Accessexponential(x,y0,A,R0)Function FileFITFUNC\EXPONENT.FDFLast Updated 11/14/00 Page 63 of 166MnMolecularFunction( )( )xc x ke A y 1Brief DescriptionMonomolecular growth model.Reference: Seber, G. A. F., Wild, C. J. 1989. Nonlinear Regression. John Wiley & Sons, Inc. p. 328Sample CurveParametersNumber: 3Names: A, xc, kMeanings: A = amplitude, xc = center, k = rateInitial Values: A = 2.0 (vary), xc = 1.0 (vary), k = 1.0 (vary)Lower Bounds: A > 0.0Upper Bounds: noneScript Accessmnmolecular(x,A,xc,k)Function FileFITFUNC\MMOLECU.FDFLast Updated 11/14/00 Page 64 of 166MnMolecular1Functionkxe A A y 2 1Brief DescriptionMonomolecular growth model.Reference: Seber, G. A. F., Wild, C. J. 1989. Nonlinear Regression. John Wiley & Sons, Inc. p. 328Sample CurveParametersNumber: 3Names: A1, A2, kMeanings: A1 = offset, A2 = coefficient, k = coefficientInitial Values: A1 = 1.0 (vary), A2 = 1.0 (vary), k = 1.0 (vary)Lower Bounds: A1 > 0.0, A2 > 0.0Upper Bounds: noneScript Accessmnmolecular1(x,A1,A2,k)Function FileFITFUNC\MMOLECU1.FDFLast Updated 11/14/00 Page 65 of 166ShahFunctionxcr bx a y + + Brief DescriptionShah model.Sample CurveParametersNumber: 4Names: a, b, c, rMeanings: a = offset, b = coefficient, c = coefficient, r = unknownInitial Values: a = 1.0 (vary), b = 1.0 (vary), c = 1.0 (vary), r = 0.5 (vary)Lower Bounds: r > 0.0Upper Bounds: r < 1.0Script Accessshah(x,a,b,c,r)Function FileFITFUNC\SHAH.FDFLast Updated 11/14/00 Page 66 of 166StirlingFunction

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.| + keb a ykx1Brief DescriptionStirling model.Sample CurveParametersNumber: 3Names: a, b, kMeanings: a = offset, b = coefficient, k = coefficientInitial Values: a = 1.0 (vary), b = 1.0 (vary), k = 1.0 (vary)Lower Bounds: noneUpper Bounds: noneScript Accessstirling(x,a,b,k)Function FileFITFUNC\STIRLING.FDFLast Updated 11/14/00 Page 67 of 166YldFertFunctionxbr a y + Brief DescriptionYield-fertilizer model in agriculture and learning curve in psychology.Sample CurveParametersNumber: 3Names: a, b, rMeanings: a = offset, b = coefficient, r = coefficientInitial Values: a = 1.0 (vary), b = 1.0 (vary), r = 0.5 (vary)Lower Bounds: r > 0.0Upper Bounds: r < 1.0Script Accessyldfert(x,a,b,r)Function FileFITFUNC\YLDFERT.FDFLast Updated 11/14/00 Page 68 of 166YldFert1Functionkxbe a y + Brief DescriptionYield-fertilizer model in agriculture and learning curve in psychology.Sample CurveParametersNumber: 3Names: a, b, kMeanings: a = offset, b = coefficient, k = coefficientInitial Values: a = 1.0 (vary), b = 1.0 (vary), k = 0.5 (vary)Lower Bounds: k > 0.0Upper Bounds: noneScript Accessyldfert1(x,a,b,k)Function FileFITFUNC\YLDFERT1.FDFLast Updated 11/14/00 Page 69 of 1664. Growth/SigmoidalBoltzmann 70Hill 71Logistic 72SGompertz 73SLogistic1 74SLogistic2 75SLogistic3 76SRichards1 77SRichards2 78SWeibull1 79SWeibull2 80Last Updated 11/14/00 Page 70 of 166BoltzmannFunction( ) 2 /2 101 AeA Aydx x x ++Brief DescriptionBoltzmann function - produces a sigmoidal curve.Sample CurveParametersNumber: 4Names: A1, A2, x0, dxMeanings: A1 = initial value, A2 = final value, x0 = center, dx = time constantInitial Values: A1 = 0.0 (vary), A2 = 1.0 (vary), x0 = 0.0 (vary), dx = 1.0 (vary)Lower Bounds: noneUpper Bounds: noneConstraintsdx ! = 0Script Accessboltzman(x,A1,A2,x0,dx)Function FileFITFUNC\BOLTZMAN.FDFLast Updated 11/14/00 Page 71 of 166HillFunctionn nnx kxV y+maxBrief DescriptionHill function.Reference: Seber, G. A. F., Wild, C. J. 1989. Nonlinear Regression. John Wiley & Sons, Inc. p. 120Sample CurveParametersNumber: 3Names: Vmax, k, nMeanings: Vmax = unknown, k = unknown, n = unknownInitial Values: Vmax = 1.0 (vary), k = 1.0 (vary), n = 1.5 (vary)Lower Bounds: Vmax > 0Upper Bounds: noneScript Accesshill(x,Vmax,k,n)Function FileFITFUNC\HILL.FDFLast Updated 11/14/00 Page 72 of 166LogisticFunction( )202 1/ 1 Ax xA Ayp ++Brief DescriptionLogistic dose response in pharmacology/chemistry.Sample CurveParametersNumber: 4Names: A1, A2, x0, pMeanings: A1 = initial value, A2 = final value, x0 = center, p =powerInitial Values: A1 = 0.0 (vary), A2 = 1.0 (vary), x0 = 1.0 (vary), p = 1.5 (vary)Lower Bounds: p > 0.0Upper Bounds: noneScript Accesslogistic(x,A1,A2,x0,p)Function FileFITFUNC\LOGISTIC.FDFLast Updated 11/14/00 Page 73 of 166SGompertzFunction( ) ( )cx x kae y expBrief DescriptionGompertz growth model for population studies, animal growth.Reference: Seber, G. A. F., Wild, C. J. 1989. Nonlinear Regression. John Wiley & Sons, Inc. pp. 330 -331Sample CurveParametersNumber: 3Names: a, xc, kMeanings: a = amplitude, xc = center, k = coefficientInitial Values: a = 1.0 (vary), xc = 1.0 (vary), k = 1.0 (vary)Lower Bounds: a > 0.0, k > 0.0Upper Bounds: noneScript Accesssgompertz(x,a,xc,k)Function FileFITFUNC\GOMPERTZ.FDFLast Updated 11/14/00 Page 74 of 166SLogistic1Function( )cx x keay +1Brief DescriptionSigmoidal logistic function, type 1.Reference: Seber, G. A. F., Wild, C. J. 1989. Nonlinear Regression. John Wiley & Sons, Inc. pp. 328 -330Sample CurveParametersNumber: 3Names: a, xc, kMeanings: a = amplitude, xc = center, k = coefficientInitial Values: a = 1.0 (vary), xc = 1.0 (vary), k = 1.0 (vary)Lower Bounds: xc > 0Upper Bounds: noneScript Accessslogistic1(x,a,xc,k)Function FileFITFUNC\SLOGIST1.FDFLast Updated 11/14/00 Page 75 of 166SLogistic2Functiona x Weyy aay/ 400 max1 +Brief DescriptionSigmoidal logistic function, type 2.Reference: Seber, G. A. F., Wild, C. J. 1989. Nonlinear Regression. John Wiley & Sons, Inc. pp. 328 -330Sample CurveParametersNumber: 3Names: y0, a, WmaxMeanings: y0 = initial value, a = amplitude, Wmax = maximum growth rateInitial Values: y0 = 0.5 (vary), a = 1.0 (vary), Wmax = 1.0 (vary)Lower Bounds: y0 > 0.0, a > 0.0, Wmax > 0.0Upper Bounds: noneScript Accessslogistic2(x,y0,a,Wmax)Function FileFITFUNC\SLOGIST2.FDFLast Updated 11/14/00 Page 76 of 166SLogistic3Functionkxbeay+1Brief DescriptionSigmoidal logistic function, type 3.Reference: Seber, G. A. F., Wild, C. J. 1989. Nonlinear Regression. John Wiley & Sons, Inc. pp. 328 -330Sample CurveParametersNumber: 3Names: a, b, kMeanings: a = amplitude, b = coefficient, k = coefficientInitial Values: a = 1.0 (vary), b = 1.0 (vary), k = 1.0 (vary)Lower Bounds: a > 0.0, b > 0.0, k >0.0Upper Bounds: noneScript Accessslogistic3(x,a,b,k)Function FileFITFUNC\SLOGIST3.FDFLast Updated 11/14/00 Page 77 of 166SRichards1Function( )[ ] ( )( )[ ] ( )1 ,1 ,1 / 111 / 11> + < d e a yd e a ydxc x k ddxc x k dBrief DescriptionSigmoidal Richards function, type 1.Reference: Seber, G. A. F., Wild, C. J. 1989. Nonlinear Regression. John Wiley & Sons, Inc. pp. 332 -337Sample CurveParametersNumber: 4Names: a, xc, d, kMeanings: a = unknown, xc = center, d = unknown, k = coefficientInitial Values: a = 1.0 (vary), xc = 1.0 (vary), d = 5 (vary), k = 0.5 (vary)Lower Bounds: a > 0.0, k > 0.0Upper Bounds: noneScript Accesssrichards1(x,a,xc,d,k)Function FileFITFUNC\SRICHAR1.FDFLast Updated 11/14/00 Page 78 of 166SRichards2Function( ) ( )[ ] ( )1 , 1 11 / 1 + d e d a y dxc x kBrief DescriptionSigmoidal Richards function, type 2.Reference: Seber, G. A. F., Wild, C. J. 1989. Nonlinear Regression. John Wiley & Sons, Inc. pp. 332 -337Sample CurveParametersNumber: 4Names: a, xc, d, kMeanings: a = unknown, xc = center, d = unknown, k = coefficientInitial Values: a = 1.0 (vary), xc = 1.0 (vary), d = 5.0 (vary), k = 1.0 (vary)Lower Bounds: a > 0.0, k > 0.0Upper Bounds: noneScript Accesssrichards2(x,a,xc,d,k)Function FileFITFUNC\SRICHAR2.FDFLast Updated 11/14/00 Page 79 of 166SWeibull1Function( ) ( )( )dcx x ke A y 1Brief DescriptionSigmoidal Weibull function, type 1.Reference: Seber, G. A. F., Wild, C. J. 1989. Nonlinear Regression. John Wiley & Sons, Inc. pp. 338 -339Sample CurveParametersNumber: 4Names: A, xc, d, kMeanings: A = amplitude, xc = center, d = power, k = coefficientInitial Values: A = 1.0 (vary), xc = 1.0 (vary), d = 5.0 (vary), k = 1.0 (vary)Lower Bounds: A > 0.0, k > 0.0Upper Bounds: noneScript Accesssweibull1(x,A,xc,d,k)Function FileFITFUNC\WEIBULL1.FDFLast Updated 11/14/00 Page 80 of 166SWeibull2Function( ) ( )dkxe B A A y Brief DescriptionSigmoidal Weibull function, type 2.Reference: Seber, G. A. F., Wild, C. J. 1989. Nonlinear Regression. John Wiley & Sons, Inc. pp. 338 -339Sample CurveParametersNumber: 4Names: a, b, d, kMeanings: a = unknown, b = unknown, d = power, k = coefficientInitial Values: a = 1.0 (vary), b = 1.0 (vary), d = 5.0 (vary), k = 1.0 (vary)Lower Bounds: a > 0.0, b > 0.0, k > 0.0Upper Bounds: noneScript Accesssweibull2(x,a,b,d,k)Function FileFITFUNC\WEIBULL2.FDFLast Updated 11/14/00 Page 81 of 1665. Hyperbola FunctionsDhyperbl 82Hyperbl 83HyperbolaGen 84HyperbolaMod 85RectHyperbola 86Last Updated 11/14/00 Page 82 of 166DhyperblFunctionx Px Px Px Px Py54321++++Brief DescriptionDouble rectangular hyperbola function.Sample CurveParametersNumber: 5Names: P1, P2, P3, P4, P5Meanings: Unknowns 1-5Initial Values: P1 = 1.0 (vary), P2 = 1.0 (vary), P3 = 1.0 (vary), P4 = 1.0 (vary), P5 = 1.0 (vary)Lower Bounds: noneUpper Bounds: noneScript Accessdhyperbl(x,P1,P2,P3,P4,P5)Function FileFITFUNC\DHYPERBL.FDFLast Updated 11/14/00 Page 83 of 166HyperblFunctionx Px Py+21Brief DescriptionHyperbola function. Also the Michaelis-Menten model in enzyme kinetics.Sample CurveParametersNumber: 2Names: P1, P2Meanings: P1 = amplitude, P2 = unknownInitial Values: P1 = 1.0 (vary), P2 = 1.0 (vary)Lower Bounds: noneUpper Bounds: noneScript Accesshyperbl(x,P1,P2)Function FileFITFUNC\HYPERBL.FDFLast Updated 11/14/00 Page 84 of 166HyperbolaGenFunction( ) dcxba y/ 11+ Brief DescriptionGeneralized hyperbola function.Reference: Ratkowksy, David A. 1990. Handbook of Nonlinear Regression Models. Marcel Dekker, Inc.4.4.7Sample CurveParametersNumber: 4Names: a, b, c, dMeanings: a = coefficient, b = coefficient, c = coefficient, d = coefficientInitial Values: a = 1.0 (vary), b = 1.0 (vary), c = 0.5, d = 0.5Lower Bounds: noneUpper Bounds: noneScript Accesshyperbolagen(x,a,b,c,d)Function FileFITFUNC\HYPERGEN.FDFLast Updated 11/14/00 Page 85 of 166HyperbolaModFunction2 1 +xxyBrief DescriptionModified hyperbola function.Reference: Ratkowksy, David A. 1990. Handbook of Nonlinear Regression Models. Marcel Dekker, Inc.4.2.18Sample CurveParametersNumber: 2Names: T1, T2Meanings: T1 = amplitude, T2 = unknownInitial Values: T1 = 1.0 (vary), T2 = 1.0 (vary)Lower Bounds: noneUpper Bounds: noneScript Accesshyperbolamod(x,T1,T2)Function FileFITFUNC\HYPERBMD.FDFLast Updated 11/14/00 Page 86 of 166RectHyperbolaFunctionbxbxa y+1Brief DescriptionRectangular hyperbola function.Reference: Ratkowksy, David A. 1990. Handbook of Nonlinear Regression Models. Marcel Dekker, Inc.4.2.16Sample CurveParametersNumber: 2Names: a, bMeanings: a = coefficient, b = coefficientInitial Values: a = 1.0 (vary), b = 1.0 (vary)Lower Bounds: noneUpper Bounds: noneScript Accessrecthyperbola(x,a,b)Function FileFITFUNC\RECTHYPB.FDFLast Updated 11/14/00 Page 87 of 1666. Logarithm FunctionsBradley 88Log2P1 89Log2P2 90Log3P1 91Logarithm 92Last Updated 11/14/00 Page 88 of 166BradleyFunction( ) ) ln( ln x b a y Brief DescriptionBradley model.Reference: Ratkowksy, David A. 1990. Handbook of Nonlinear Regression Models. Marcel Dekker, Inc.3.3.7Sample CurveParametersNumber: 2Names: a, bMeanings: a = unknown, b = unknownInitial Values: a = 1.0 (vary), b = 1.0 (vary)Lower Bounds: noneUpper Bounds: noneScript Accessbradley(x,a,b)Function FileFITFUNC\BRADLEY.FDFLast Updated 11/14/00 Page 89 of 166Log2P1Function( ) a x b y lnBrief DescriptionTwo-parameter logarithm function.Reference: Ratkowksy, David A. 1990. Handbook of Nonlinear Regression Models. Marcel Dekker, Inc.4.2.1Sample CurveParametersNumber: 2Names: a, bMeanings: a = offset, b = coefficientInitial Values: a = 1.0 (vary), b = 1.0 (vary)Lower Bounds: noneUpper Bounds: noneScript Accesslog2p1(x,a,b)Function FileFITFUNC\LOG2P1.FDFLast Updated 11/14/00 Page 90 of 166Log2P2Function( ) bx a y + lnBrief DescriptionTwo-parameter logarithm.Reference: Ratkowksy, David A. 1990. Handbook of Nonlinear Regression Models. Marcel Dekker, Inc.4.2.3Sample CurveParametersNumber: 2Names: a, bMeanings: a = offset, b = coefficientInitial Values: a = 1.0 (vary), b = 1.0 (vary)Lower Bounds: noneUpper Bounds: noneScript Accesslog2p2(x,a,b)Function FileFITFUNC\LOG2P2.FDFLast Updated 11/14/00 Page 91 of 166Log3P1Function( ) c x b a y + lnBrief DescriptionThree-parameter logarithm function.Reference: Ratkowksy, David A. 1990. Handbook of Nonlinear Regression Models. Marcel Dekker, Inc.4.3.32Sample CurveParametersNumber: 3Names: a, b, cMeanings: a = coefficient, b = coefficient, c = coefficientInitial Values: a = 1.0 (vary), b = 1.0 (vary), c = 0.5Lower Bounds: noneUpper Bounds: noneScript Accesslog3p1(x,a,b,c)Function FileFITFUNC\LOG3P1.FDFLast Updated 11/14/00 Page 92 of 166LogarithmFunction( ) A x y lnBrief DescriptionOne-parameter logarithm.Reference: Ratkowksy, David A. 1990. Handbook of Nonlinear Regression Models. Marcel Dekker, Inc.4.1.1Sample CurveParametersNumber: 1Names: AMeanings: A = centerInitial Values: A = 1.0 (vary)Lower Bounds: noneUpper Bounds: noneScript Accesslogarithm(x,A)Function FileFITFUNC\LOGARITH.FDFLast Updated 11/14/00 Page 93 of 1667. Peak FunctionsAsym2Sig 94Beta 95CCE 96ECS 97Extreme 98Gauss 99GaussAmp 100GaussMod 101GCAS 102Giddings 103InvsPoly 104LogNormal 105Logistpk 106Lorentz 107PearsonVII 108PsdVoigt1 109PsdVoigt2 110Voigt 111Weibull3 112Last Updated 11/14/00 Page 94 of 166Asym2SigFunction

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.|+++ + 31212 / 2 / 011111ww x xww x x c ce eA y yBrief DescriptionAsymmetric double sigmoidal.Sample CurveParametersNumber: 6Names: y0, xc, A, w1, w2, w3Meanings: y0 = offset, xc = center, A = amplitude, w1 = width, w2 = width, w3 = widthInitial Values: y0 = 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: w1 > 0.0, w2 > 0.0, w3 > 0.0Upper Bounds: noneScript Accessasym2sig(x,y0,xc,A,w1,w2,w3)Function FileFITFUNC\ASYMDBLS.FDFLast Updated 11/14/00 Page 95 of 166BetaFunction11 33 211 23 203 2121121 ]]]

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.| ++ + wcwcwx xww wwx xww wA y yBrief DescriptionThe beta function.Sample CurveParametersNumber: 6Names: y0, xc, A, w1, w2, w3Meanings: y0 = offset, xc = center, A = amplitude, w1 = width, w2 = width, w3 = widthInitial Values: y0 = 0.0 (vary), xc = 1.0 (vary), A = 5.0 (vary), w1 = 5.0 (vary), w2 = 2.0 (vary), w3 = 2.0(vary)Lower Bounds: w1 > 0.0, w2 > 1.0, w3 > 1.0Upper Bounds: noneScript Accessbeta(x,y0,xc,A,w1,w2,w3)Function FileFITFUNC\BETA.FDFLast Updated 11/14/00 Page 96 of 166CCEFunction( )( ) ( ) ( ) ( ) ( ) ( )]]]]

+ + + 3 3 3215 . 02 220tanh 1 5 . 0 1 c ccx x x x kCwx xe x x k B e A y yBrief DescriptionChesler-Cram peak function for use in chromatography.Sample CurveParametersNumber: 9Names: y0, xc1, A, w, k2, xc2, B, k3, xc3Meanings: y0 = offset, xc1 = unknown, A = unknown, w = unknown, k2 = unknown, xc2 = unknown, B =unknown, k3 = unknown, xc3 = unknownInitial Values: y0 = 0.0 (vary), xc1 = 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 > 0.0Upper Bounds: noneScript Accesscce(x,y0,xc1,A,w,k2,xc2,B,k3,xc3)Function FileFITFUNC\CHESLECR.FDFLast Updated 11/14/00 Page 97 of 166ECSFunction( ) ( )( )''

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.| + ++ + ++ 15 45 15! 6103 6! 43! 3122 4 6233 4 4 2 35 . 002z z zaz zaz zaewAy y zwhere wx xz cBrief DescriptionEdgeworth-Cramer peak function for use in chromatography.Sample CurveParametersNumber: 6Names: y0, xc, A, w, a3, a4Meanings: y0 = offset, xc = center, A = amplitude, w = width, a3 = unknown, a4 = unknownInitial Values: y0 = 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 > 0.0, w > 0.0Upper Bounds: noneScript Accessecs(x,y0,xc,A,w,a3,a4)Function FileFITFUNC\EDGWTHCR.FDFLast Updated 11/14/00 Page 98 of 166ExtremeFunction]]]

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.| + 1 exp0wx xwx xAe y y c cBrief DescriptionExtreme function in statistics.Sample CurveParametersNumber: 4Names: y0, xc, w, AMeanings: y0 = offset, xc = center, w = width, A = amplitudeInitial Values: y0 = 0.0 (vary), xc = 1.0 (vary), w = 1.0 (vary), A = 1.0 (vary)Lower Bounds: w > 0.0Upper Bounds: noneScript Accessextreme(x,y0,xc,w,A)Function FileFITFUNC\EXTREME.FDFLast Updated 11/14/00 Page 99 of 166GaussFunction( )22202 /wx x cewAy y+ Brief DescriptionArea version of Gaussian function.Sample CurveParametersNumber: 4Names: y0, xc, w, AMeanings: y0 = offset, xc = center, w = width, A = areaInitial Values: y0 = 0.0 (vary), xc = 0.0 (vary), w = 1.0 (vary), A = 10 (vary)Lower Bounds: w > 0.0Upper Bounds: noneScript Accessgauss(x,y0,xc,w,A)Function FileFITFUNC\GAUSS.FDFLast Updated 11/14/00 Page 100 of 166GaussAmpFunction( )2220wx x cAe y y+ Brief DescriptionAmplitude version of Gaussian peak function.Sample CurveParametersNumber: 4Names: y0, xc, w, AMeanings: y0 = offset, xc = center, w = width, A = areaInitial Values: y0 = 0.0 (vary), xc = 0.0 (vary), w = 1.0 (vary), A = 10 (vary)Lower Bounds: w > 0.0Upper Bounds: noneScript Accessgaussamp(x,y0,xc,w,A)Function FileFITFUNC\GAUSSAMP.FDFLast Updated 11/14/00 Page 101 of 166GaussModFunction

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.|+ z ytx xtwdy e etAy x fc22100202021) (where 0twwx xz cBrief DescriptionExponentially modified Gaussian peak function for use in chromatography.Sample CurveParametersNumber: 5Names: y0, A, xc, w, t0Meanings: y0 = offset, A = amplitude, xc = center, w = width, t0 = unknownInitial Values: y0 = 0.0 (vary), A = 1.0 (vary), xc = 0.0 (vary), w = 1.0 (vary), t0 = 0.05 (vary)Lower Bounds: w > 0.0, t0 > 0.0Upper Bounds: noneScript Accessgaussmod(x,y0,A,xc,w,t0)Function FileFITFUNC\GAUSSMOD.FDFLast Updated 11/14/00 Page 102 of 166GCASFunction( ),`

.|+ + z HiaewAy z f iii z432 /0!12) (23 633 4433+ z z Hz z Hwx xz cBrief DescriptionGram-Charlier peak function for use in chromatography.Sample CurveParametersNumber: 6Names: y0, xc, A, w, a3, a4Meanings: y0 = offset, xc = center, A = amplitude, w = width, a3 = unknown, a4 = unknownInitial Values: y0 = 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 > 0.0Upper Bounds: noneScript Accessgcas(x,y0,xc,A,w,a3,a4)Function FileFITFUNC\GRMCHARL.FDFLast Updated 11/14/00 Page 103 of 166GiddingsFunctionwx xc ccewx xIxxwAy y

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.|+ 21 0Brief DescriptionGiddings peak function for use in chromatography.Sample CurveParametersNumber: 4Names: y0, xc, w, AMeanings: y0 = offset, xc = center, w = width, A = areaInitial Values: y0 = 0.0 (vary), xc = 1.0 (vary), w = 1.0 (vary), A = 1.0 (vary)Lower Bounds: w > 0.0Upper Bounds: noneScript Accessgiddings(x,y0,xc,w,A)Function FileFITFUNC\GIDDINGS.FDFLast Updated 11/14/00 Page 104 of 166InvsPolyFunction63422102 2 2 1 ,`

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.| ++ wx xAwx xAwx xAAy yc c cBrief DescriptionInverse polynomial peak function with center.Sample CurveParametersNumber: 7Names: y0, xc, w, A, A1, A2, A3Meanings: y0 = offset, xc = center, w = width, A = amplitude, A1 = coefficient, A2 = coefficient, A3 =coefficientInitial Values: y0 = 0.0 (vary), xc = 0.0 (vary), w = 1.0 (vary), A = 1.0 (vary), A1 = 0.0 (vary), A2 = 0.0(vary), A3 = 0.0 (vary)Lower Bounds: w > 0.0, A1 0.0, A2 0.0, A3 0.0Upper Bounds: noneScript Accessinvspoly(x,y0,xc,w,A,A1,A2,A3)Function FileFITFUNC\INVSPOLY.FDFLast Updated 11/14/00 Page 105 of 166LogNormalFunction[ ]222/ ln02wx x cewxAy y+ Brief DescriptionLog-Normal function.Sample CurveParametersNumber: 4Names: y0, xc, w, AMeanings: y0 = offset, xc = center, w = width, A = amplitudeInitial Values: y0 = 0.0 (vary), xc = 1.0 (vary), w = 1.0 (vary), A = 1.0 (vary)Lower Bounds: xc > 0, w > 0Upper Bounds: noneScript Accesslognormal(x,y0,xc,w,A)Function FileFITFUNC\LOGNORM.FDFLast Updated 11/14/00 Page 106 of 166LogistpkFunction2 014

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.|++ wxc xwxc xeAey yBrief DescriptionLogistic peak function.Sample CurveParametersNumber: 4Names: y0, xc, w, AMeanings: y0 = offset, xc = center, w = width, A = amplitudeInitial Values: y0 = 0.0 (vary), xc = 1.0 (vary), w = 1.0 (vary), A = 1.0 (vary)Lower Bounds: w > 0.0Upper Bounds: noneScript Accesslogistpk(x,y0,xc,w,A)Function FileFITFUNC\LOGISTPKLast Updated 11/14/00 Page 107 of 166LorentzFunction( )2 2 042w x xw Ay yc + + Brief DescriptionLorentzian peak function.Sample CurveParametersNumber: 4Names: y0, xc, w, AMeanings: y0 = offset, xc = center, w = width, A = areaInitial Values: y0 = 0.0 (vary), xc = 0.0 (vary), w = 1.0 (vary), A = 1.0 (vary)Lower Bounds: w > 0.0Upper Bounds: noneScript Accesslorentz(x,y0,xc,w,A)Function FileFITFUNC\LORENTZ.FDFLast Updated 11/14/00 Page 108 of 166PearsonVIIFunction( )( ) ( )mucmumu x xw ee muA ymu ]]]

+ 22/ 1) 2 / 1 () 1 2 (1 24 12/ 1Brief DescriptionPearson VII peak function.Sample CurveParametersNumber: 4Names: xc, A, w, muMeanings: xc = center, A = amplitude, w = width, mu = profile shape factorInitial Values: xc = 0.0 (vary), A = 1.0 (vary), w = 1.0 (vary), mu = 1.0 (vary)Lower Bounds: A > 0.0, w > 0.0, mu > 0.0Upper Bounds: noneScript Accesspearson7(x,xc,A,w,mu)Function FileFITFUNC\PEARSON7.FDFLast Updated 11/14/00 Page 109 of 166PsdVoigt1Function( ) ( ) ( )]]]]

++ + 222 ln 42 2 02 ln 4142 cx xwucu ewmw x xwm A y y Brief DescriptionPseudo-Voigt peak function type 1.Sample CurveParametersNumber: 5Names: y0, xc, A, w, muMeanings: y0 = offset, xc = center, A = amplitude, w = width, mu = profile shape factorInitial Values: y0 = 0.0 (vary), xc = 0.0 (vary), A = 1.0 (vary), w = 1.0 (vary), mu = 0.5 (vary)Lower Bounds: w > 0.0Upper Bounds: noneScript Accesspsdvoigt1(x,y0,xc,A,w,mu)Function FileFITFUNC\PSDVGT1.FDFLast Updated 11/14/00 Page 110 of 166PsdVoigt2Function( ) ( ) ( )]]]]

++ + 222 ln 42 202 ln 4142 cGx xwGuL cLu ewmw x xwm A y yBrief DescriptionPseudo-Voigt peak function type 2.Sample CurveParametersNumber: 6Names: y0, xc, A, wG, wL, muMeanings: y0 = offset, xc = center, A = amplitude, wG = width, wL = width, mu = profile shape factorInitial 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 > 0.0, wL > 0.0Upper Bounds: noneScript Accesspsdvoigt2(x,y0,xc,A,wG,wL,mu)Function FileFITFUNC\PSDVGT2.FDFLast Updated 11/14/00 Page 111 of 166VoigtFunction

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.| + dttwx xwwewwA y yGcGLtGL2 2 2 2 / 3 02 ln 4 2 ln2 ln 22Brief DescriptionVoigt peak function.Sample CurveParametersNumber: 5Names: y0, xc, A, wG, wLMeanings: y0 = offset, xc = center, A = amplitude, wG = Gaussian width, wL = Lorentzian widthInitial Values: y0 = 0.0 (vary), xc = 0.0 (vary), A = 1.0 (vary), wG = 1.0 (vary), wL = 1.0 (vary)Lower Bounds: wG > 0.0, wL > 0.0Upper Bounds: noneScript Accessvoigt5(x,y0,xc,A,wG,wL)Function FileFITFUNC\VOIGT5.FDFLast Updated 11/14/00 Page 112 of 166Weibull3Function[ ] [ ]

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.| +22 22222111220122111wwSwwwwcwe SwwA y ywwwx xSBrief DescriptionWeibull peak function.Sample CurveParametersNumber: 5Names: y0, xc, A, w1, w2Meanings: y0 = offset, xc = center, A = amplitude, w1 = width, w2 = widthInitial Values: y0 = 0.0 (vary), xc = 0.0 (vary), A = 1.0 (vary), w1 = 1.0 (vary), w2 = 1.0 (vary)Lower Bounds: w1 > 0.0, w2 > 0.0Upper Bounds: noneScript Accessweibull3(x,y0,xc,A,w1,w2)Function FileFITFUNC\WEIBULL3.FDFLast Updated 11/14/00 Page 113 of 1668. Pharmacology FunctionsBiphasic 114DoseResp 115OneSiteBind 116OneSiteComp 117TwoSiteBind 118TwoSiteComp 119Last Updated 11/14/00 Page 114 of 166BiphasicFunction( )( ) ( )( )( )( )2 )* 2 _ 0 (min 2 max1 * 1 _ 0min 1 maxmin10 1 10 1 h x x h x xA A A AA y ++++ Brief DescriptionBiphasic sigmoidal dose response (7 parameters logistic equation).Sample CurveParametersNumber: 7Names: Amin, Amax1, Amax2, x0_1, x0_2, h1, h2Meanings: Amin = bottom asymptote, Amax1 = first top asymptote, Amax2 = second top asymptote, x0_1= first median, x0_2 = second median, h1 = slope, h2 = slopeInitial Values: Amin = 0.0 (vary), Amax1 = 1.0 (vary), Amax2 = 1.0 (vary), x0_1 = 1.0 (vary), x0_2 = 10.0(vary), h1 = 1.0 (vary), h2 = 1.0 (vary)Lower Bounds: noneUpper Bounds: noneScript Accessresponse2(x,Amin,Amax1,Amax2,x0_1,x0_2,h1,h2)Function FileFITFUNC\BIPHASIC.FDFLast Updated 11/14/00 Page 115 of 166DoseRespFunction( )p x xA AA y++ 0log1 2110 1Brief DescriptionDose-response curve with variable Hill slope given by parameter 'p'.Sample CurveParametersNumber: 4Names: A1, A2, LOGx0, pMeanings: A1 = bottom asymptote, A2 = top asymptote, LOGx0 = center, p = hill slopeInitial Values: A1 = 1.0 (vary), A2 = 100.0 (vary), LOGx0 = -5.0 (vary), p = 1.0 (vary)Lower Bounds: noneUpper Bounds: noneScript Accessresponse1(x,A1,A2,LOGx0,p)Function FileFITFUNC\DRESP.FDFLast Updated 11/14/00 Page 116 of 166OneSiteBindFunctionx Kx By+1maxBrief DescriptionOne site direct binding. Rectangular hyperbola, connects to isotherm or saturation curve.Sample CurveParametersNumber: 2Names: Bmax, K1Meanings: Bmax = top asymptote, K1 = medianInitial Values: Bmax = 1.0 (vary), K1 = 1.0 (vary)Lower Bounds: noneUpper Bounds: noneScript Accessbinding1(x,Bmax,K1)Function FileFITFUNC\BIND1.FDFLast Updated 11/14/00 Page 117 of 166OneSiteCompFunction( )0log2 1210 1 x xA AA y++ Brief DescriptionOne site competition curve. Dose-response curve with Hill slope equal to -1.Sample CurveParametersNumber: 3Names: A1, A2, log(x0)Meanings: A1 = top asymptote, A2 = bottom asymptote, log(x0) = centerInitial Values: A1 = 10.0 (vary), A2 = 1.0 (vary), log(x0) = 1.0 (vary)Lower Bounds: noneUpper Bounds: noneScript Accesscompetition1(x,A1,A2,LOGx0)Function FileFITFUNC\COMP1.FDFLast Updated 11/14/00 Page 118 of 166TwoSiteBindFunctionx Kx Bx Kx By+++22 max11 maxBrief DescriptionTwo site binding curve.Sample CurveParametersNumber: 4Names: Bmax1, Bmax2, k1, k2Meanings: Bmax1 = first top asymptote, Bmax2 = second top asymptote, k1 = first median, k2 = secondmedianInitial Values: Bmax1 = 1.0 (vary), Bmax2 = 1.0 (vary), k1 = 1.0 (vary), k2 = 1.0 (vary)Lower Bounds: noneUpper Bounds: noneScript Accessbinding2(x,Bmax1,Bmax2,k1,k2)Function FileFITFUNC\BIND2.FDFLast Updated 11/14/00 Page 119 of 166TwoSiteCompFunction( )( )( )( )( )02 01log2 1log2 1210 1110 1 x x x xf A A f A AA y + +++ Brief DescriptionTwo site competition.Sample CurveParametersNumber: 5Names: A1, A2, log(x0_1), log(x0_2), fMeanings: A1 = top asymptote, A2 = bottom asymptote, log(x0_1) = first center, log(x0_2) = secondcenter, f = fractionInitial Values: A1 = 10.0 (vary), A2 = 1.0 (vary), log(x0_1) = 1.0 (vary), log(x0_2) = 2.0 (vary), f = 0.5(vary)Lower Bounds: noneUpper Bounds: noneScript Accesscompetition2(x,A1,A2,LOGx0_1,LOGx0_2,f)Function FileFITFUNC\COMP2.FDFLast Updated 11/14/00 Page 120 of 1669. Power FunctionsAllometric1 121Allometric2 122Asym2Sig 123Belehradek 124BlNeld 125BlNeldSmp 126FreundlichEXT 127Gunary 128Harris 129LangmuirEXT1 130LangmuirEXT2 131Pareto 132Pow2P1 133Pow2P2 134Pow2P3 135Power 136Power0 137Power1 138Power2 139Last Updated 11/14/00 Page 121 of 166Allometric1Functionbax y Brief DescriptionClassical Freundlich model. Has been used in the study of allometry.Sample CurveParametersNumber: 2Names: a, bMeanings: a = coefficient, b = powerInitial Values: a = 1.0 (vary), b = 0.5 (vary)Lower Bounds: noneUpper Bounds: noneScript Accessallometric1(x,a,b)Function FileFITFUNC\ALLOMET1.FDFLast Updated 11/14/00 Page 122 of 166Allometric2Functioncbx a y + Brief DescriptionAn extension of classical Freundlich model.Sample CurveParametersNumber: 3Names: a, b, cMeanings: a = offset, b = coefficient, c = powerInitial Values: a = 1.0 (vary), b = 1.0 (vary), c = 0.5 (vary)Lower Bounds: noneUpper Bounds: noneScript Accessallometric2(x,a,b,c)Function FileFITFUNC\ALLOMET2.FDFLast Updated 11/14/00 Page 123 of 166Asym2SigFunction

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.|+++ + 31212 / 2 / 011111ww x xww x x c ce eA y yBrief DescriptionAsymmetric double sigmoidal.Sample CurveParametersNumber: 6Names: y0, xc, A, w1, w2, w3Meanings: y0 = offset, xc = center, A = amplitude, w1 = width, w2 = width, w3 = widthInitial Values: y0 = 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: w1 > 0.0, w2 > 0.0, w3 > 0.0Upper Bounds: noneScript Accessasym2sig(x,y0,xc,A,w1,w2,w3)Function FileFITFUNC\ASYMDBLS.FDFLast Updated 11/14/00 Page 124 of 166BelehradekFunction( )cb x a y Brief DescriptionBelehradek model.Sample CurveParametersNumber: 3Names: a, b, cMeanings: a = coefficient, b = position, c = powerInitial Values: a = 1.0 (vary), b = 1.0 (vary), c = 0.5Lower Bounds: noneUpper Bounds: noneScript Accessbelehradek(x,a,b,c)Function FileFITFUNC\BELEHRAD.FDFLast Updated 11/14/00 Page 125 of 166BlNeldFunction( ) cfbx a y/ 1 + Brief DescriptionBleasdale-Nelder model.Sample CurveParametersNumber: 4Names: a, b, c, fMeanings: a = coefficient, b = coefficient, c = coefficient, f = powerInitial Values: a = 1.0 (vary), b = 1.0 (vary), c = 0.5, f = 1.0Lower Bounds: noneUpper Bounds: noneScript Accessblneld(x,a,b,c,f)Function FileFITFUNC\BLNELD.FDFLast Updated 11/14/00 Page 126 of 166BlNeldSmpFunction( ) cbx a y/ 1 + Brief DescriptionSimplified Bleasdale-Nelder model.Sample CurveParametersNumber: 3Names: a, b, cMeanings: a = coefficient, b = coefficient, c = coefficientInitial Values: a = 1.0 (vary), b = 1.0 (vary), c = 0.5Lower Bounds: noneUpper Bounds: noneScript Accessblneldsmp(x,a,b,c)Function FileFITFUNC\BLNELDSP.FDFLast Updated 11/14/00 Page 127 of 166FreundlichEXTFunctioncbxax y Brief DescriptionExtended Freundlich model.Sample CurveParametersNumber: 3Names: a, b, cMeanings: a = coefficient, b = coefficient, c = powerInitial Values: a = 1.0 (vary), b = 1.0 (vary), c = 0.5Lower Bounds: noneUpper Bounds: noneScript Accessfreundlichext(x,a,b,c)Function FileFITFUNC\FRENDEXT.FDFLast Updated 11/14/00 Page 128 of 166GunaryFunctionx c bx axy+ +Brief DescriptionGunary model.Sample CurveParametersNumber: 3Names: a, b, cMeanings: a = coefficient, b = coefficient, c = coefficientInitial Values: a = 1.0 (vary), b = 1.0 (vary), c = 0.5Lower Bounds: noneUpper Bounds: noneScript Accessgunary(x,a,b,c)Function FileFITFUNC\GUNARY.FDFLast Updated 11/14/00 Page 129 of 166HarrisFunction( )1 + cbx a yBrief DescriptionFarazdaghi-Harris model for use in yield-density study.Sample CurveParametersNumber: 3Names: a, b, cMeanings: a = coefficient, b = coefficient, c = powerInitial Values: a = 1.0 (vary), b = 1.0 (vary), c = 0.5Lower Bounds: noneUpper Bounds: noneScript Accessharris(x,a,b,c)Function FileFITFUNC\HARRIS.FDFLast Updated 11/14/00 Page 130 of 166LangmuirEXT1Functionccbxabxy+111Brief DescriptionExtended Langmuir model.Sample CurveParametersNumber: 3Names: a, b, cMeanings: a = coefficient, b = coefficient, c = coefficientInitial Values: a = 1.0 (vary), b = 1.0 (vary), c = 0.5Lower Bounds: noneUpper Bounds: noneScript Accesslangmuirext1(x,a,b,c)Function FileFITFUNC\LANGEXT1.FDFLast Updated 11/14/00 Page 131 of 166LangmuirEXT2Function11+cbx ayBrief DescriptionExtended Langmuir model.Sample CurveParametersNumber: 3Names: a, b, cMeanings: a = coefficient, b = coefficient, c = coefficientInitial Values: a = 1.0 (vary), b = 1.0 (vary), c = 0.5Lower Bounds: noneUpper Bounds: noneScript Accesslangmuirext2(x,a,b,c)Function FileFITFUNC\LANGEXT2.FDFLast Updated 11/14/00 Page 132 of 166ParetoFunctionAxy11 Brief DescriptionPareto function.Sample CurveParametersNumber: 1Names: AMeanings: A = coefficientInitial Values: A = 1.0 (vary)Lower Bounds: noneUpper Bounds: noneScript Accesspareto(x,A)Function FileFITFUNC\PARETO.FDFLast Updated 11/14/00 Page 133 of 166Pow2P1Function( )bx a y 1Brief DescriptionTwo-parameter power function.Sample CurveParametersNumber: 2Names: a, bMeanings: a = coefficient, b = powerInitial Values: a = 1.0 (vary), b = 1.0 (vary)Lower Bounds: noneUpper Bounds: noneScript Accesspow2p1(x,a,b)Function FileFITFUNC\POW2P1.FDFLast Updated 11/14/00 Page 134 of 166Pow2P2Function( )bx a y + 1Brief DescriptionTwo-parameter power function.Sample CurveParametersNumber: 2Names: a, bMeanings: a = coefficient, b = powerInitial Values: a = 1.0 (vary), b = 1.0 (vary)Lower Bounds: noneUpper Bounds: noneScript Accesspow2p2(x,a,b)Function FileFITFUNC/POW2P2.FDFLast Updated 11/14/00 Page 135 of 166Pow2P3Function( )baxy+ 111Brief DescriptionTwo-parameter power function.Sample CurveParametersNumber: 2Names: a, bMeanings: a = coefficient, b = powerInitial Values: a = 1.0 (vary), b = 1.0 (vary)Lower Bounds: noneUpper Bounds: noneScript Accesspow2p3(x,a,b)Function FileFITFUNC\POW2P3.FDFLast Updated 11/14/00 Page 136 of 166PowerFunctionAx y Brief DescriptionOne-parameter power function.Sample CurveParametersNumber: 1Names: AMeanings: A = powerInitial Values: A = 1.0 (vary)Lower Bounds: noneUpper Bounds: noneScript Accesspower(x,A)Function FileFITFUNC\POWER.FDFLast Updated 11/14/00 Page 137 of 166Power0Functionpcx x A y y + 0Brief DescriptionSymmetric power function with offset.Sample CurveParametersNumber: 4Names: y0, xc, A, PMeanings: y0 = offset, xc = center, A = amplitude, P = powerInitial Values: y0 = 0.0 (vary), xc = 5.0 (vary), A = 1.0 (vary), P = 0.5 (vary)Lower Bounds: A > 0.0Upper Bounds: noneScript Accesspower0(x,y0,xc,A,P)Function FileFITFUNC\POWER0.FDFLast Updated 11/14/00 Page 138 of 166Power1Functionpcx x A y Brief DescriptionSymmetric power function.Sample CurveParametersNumber: 3Names: xc, A, PMeanings: xc = center, A = amplitude, P = powerInitial Values: xc = 0.0 (vary), A = 1.0 (vary), P = 2.0 (vary)Lower Bounds: A > 0.0, P > 0.0Upper Bounds: noneScript Accesspower1(x,xc,A,P)Function FileFITFUNC\POWER1.FDFLast Updated 11/14/00 Page 139 of 166Power2FunctioncPuccPlcx x x x A yx x x x A y> < ,,Brief DescriptionAsymmetric power function.Sample CurveParametersNumber: 4Names: xc, A, pl, puMeanings: xc = center, A = amplitude, p1 = power, pu = powerInitial Values: xc = 0.0 (vary), A = 1.0 (vary), p1 = 2.0 (vary), pu = 2.0 (vary)Lower Bounds: A > 0.0, p1 > 0.0, pu > 0.0Upper Bounds: noneScript Accesspower2(x,xc,A,pl,pu)Function FileFITFUNC\POWER2.FDFLast Updated 11/14/00 Page 140 of 16610. Rational FunctionsBET 141BETMod 142Holliday 143Holliday1 144Nelder 145Rational0 146Rational1 147Rational2 148Rational3 149Rational4 150Reciprocal 151Reciprocal0 152Reciprocal1 153ReciprocalMod 154Last Updated 11/14/00 Page 141 of 166BETFunction( ) ( )21 2 1 x b x babxy +Brief DescriptionBET model.Sample CurveParametersNumber: 2Names: a, bMeanings: a = coefficient, b = coefficientInitial Values: a = 1.0 (vary), b = 5.0 (vary)Lower Bounds: noneUpper Bounds: noneScript Accessbet(x,a,b)Function FileFITFUNC\BET.FDFLast Updated 11/14/00 Page 142 of 166BETModFunction( )2x b a bx axy+ +Brief DescriptionModified BET model.Sample CurveParametersNumber: 2Names: a, bMeanings: a = coefficient, b = coefficientInitial Values: a = 1.0 (vary), b = 5.0 (vary)Lower Bounds: noneUpper Bounds: noneScript Accessbetmod(x,a,b)Function FileFITFUNC\BETMOD.FDFLast Updated 11/14/00 Page 143 of 166HollidayFunction( )12 + + cx bx a yBrief DescriptionHolliday model - a Yield-density model for use in agriculture.Sample CurveParametersNumber: 3Names: a, b, cMeanings: a = coefficient, b = coefficient, c = coefficientInitial Values: a = 1.0 (vary), b = 1.0 (vary), c = 1.0 (vary)Lower Bounds: noneUpper Bounds: noneScript Accessholliday(x,a,b,c)Function FileFITFUNC\HOLLIDAY.FDFLast Updated 11/14/00 Page 144 of 166Holliday1Function2cx bx aay+ +Brief DescriptionExtended Holliday model.Sample CurveParametersNumber: 3Names: a, b, cMeanings: a = coefficient, b = coefficient, c = coefficientInitial Values: a = 1.0 (vary), b = 1.0 (vary), c = 0.5Lower Bounds: noneUpper Bounds: noneScript Accessholliday1(x,a,b,c)Function FileFITFUNC\HOLLIDY1.FDFLast Updated 11/14/00 Page 145 of 166NelderFunction( ) ( )22 1 0 a x b a x b ba xy+ + + ++Brief DescriptionNelder model - a Yield-fertilizer model in agriculture.Sample CurveParametersNumber: 4Names: a, b0, b1, b2Meanings: a = unknown, b0 = unknown, b1 = unknown, b2 = unknownInitial Values: a = 1.0 (vary), b0 = 1.0 (vary), b1 = 1.0 (vary), b2 = 1.0 (vary)Lower Bounds: noneUpper Bounds: noneScript Accessnelder(x,a,b0,b1,b2)Function FileFITFUNC\NELDER.FDFLast Updated 11/14/00 Page 146 of 166Rational0Functionaxcx by++1Brief DescriptionRational function, type 0.Reference: Ratkowksy, David A. 1990. Handbook of Nonlinear Regression Models. Marcel Dekker, Inc.4.3.24Sample CurveParametersNumber: 3Names: a, b, cMeanings: a = coefficient, b = coefficient, c = coefficientInitial Values: a = 1.0 (vary), b = 1.0 (vary), c = 0.5Lower Bounds: noneUpper Bounds: noneScript Accessrational0(x,a,b,c)Function FileFITFUNC\RATION0.FDFLast Updated 11/14/00 Page 147 of 166Rational1Functionbx acxy++1Brief DescriptionRational function, type 1.Sample CurveParametersNumber: 3Names: a, b, cMeanings: a = coefficient, b =coefficient, c = coefficientInitial Values: a = 1.0 (vary), b = 1.0 (vary), c = 0.5Lower Bounds: noneUpper Bounds: noneScript Accessrational1(x,a,b,c)Function FileFITFUNC\RATION1.FDFLast Updated 11/14/00 Page 148 of 166Rational2Functionx acx by++Brief DescriptionRational function, type 2.Sample CurveParametersNumber: 3Names: a, b, cMeanings: a = coefficient, b = coefficient, c = coefficientInitial Values: a = 1.0 (vary), b = 1.0 (vary), c = 0.5Lower Bounds: noneUpper Bounds: noneScript Accessrational2(x,a,b,c)Function FileFITFUNC\RATION2.FDFLast Updated 11/14/00 Page 149 of 166Rational3Functioncx ax by++Brief DescriptionRational function, type 3.Sample CurveParametersNumber: 3Names: a, b, cMeanings: a = coefficient, b = coefficient, c = coefficientInitial Values: a = 1.0 (vary), b = 1.0 (vary), c = 0.5Lower Bounds: noneUpper Bounds: noneScript Accessrational3(x,a,b,c)Function FileFITFUNC\RATION3.FDFLast Updated 11/14/00 Page 150 of 166Rational4Functiona xbc y++ Brief DescriptionRational function, type 4.Sample CurveParametersNumber: 3Names: a, b, cMeanings: a = coefficient, b = coefficient, c = coefficientInitial Values: a = 1.0 (vary), b = 1.0 (vary), c = 0.5Lower Bounds: noneUpper Bounds: noneScript Accessrational4(x,a,b,c)Function FileFITFUNC\RATION4.FDFLast Updated 11/14/00 Page 151 of 166ReciprocalFunctionbx ay+1Brief DescriptionTwo-parameter linear reciprocal function.Sample CurveParametersNumber: 2Names: a, bMeanings: a = coefficient, b = coefficientInitial Values: a = 1.0 (vary), b = 1.0 (vary)Lower Bounds: noneUpper Bounds: noneScript Accessreciprocal(x,a,b)Function FileFITFUNC\RECIPROC.FDFLast Updated 11/14/00 Page 152 of 166Reciprocal0FunctionAxy+11Brief DescriptionOne-parameter linear reciprocal function.Sample CurveParametersNumber: 1Names: AMeanings: A = coefficientInitial Values: A = 1.0 (vary)Lower Bounds: noneUpper Bounds: noneScript Accessreciprocal0(x,A)Function FileFITFUNC\RECIPR0.FDFLast Updated 11/14/00 Page 153 of 166Reciprocal1FunctionA xy+1Brief DescriptionOne-parameter linear reciprocal function.Sample CurveParametersNumber: 1Names: AMeanings: A = positionInitial Values: A = 1.0 (vary)Lower Bounds: noneUpper Bounds: noneScript Accessreciprocal1(x,A)Function FileFITFUNC\RECIPR1.FDFLast Updated 11/14/00 Page 154 of 166ReciprocalModFunctionbxay+1Brief DescriptionTwo parameter linear reciprocal function.Sample CurveParametersNumber: 2Names: a, bMeanings: a = coefficient, b = coefficientInitial Values: a = 1.0 (vary), b = 1.0 (vary)Lower Bounds: noneUpper Bounds: noneScript Accessreciprocalmod(x,a,b)Function FileFITFUNC\RECIPMOD.FDFLast Updated 11/14/00 Page 155 of 16611. Spectroscopy FunctionsGaussAmp 156InvsPoly 157Lorentz 158PearsonVII 159PsdVoigt1 160PsdVoigt2 161Voigt 162Last Updated 11/14/00 Page 156 of 166GaussAmpFunction( )2220wx x cAe y y+ Brief DescriptionAmplitude version of Gaussian peak function.Sample CurveParametersNumber: 4Names: y0, xc, w, AMeanings: y0 = offset, xc = center, w = width, A = areaInitial Values: y0 = 0.0 (vary), xc = 0.0 (vary), w = 1.0 (vary), A = 10 (vary)Lower Bounds: w > 0.0Upper Bounds: noneScript Accessgaussamp(x,y0,xc,w,A)Function FileFITFUNC\GAUSSAMP.FDFLast Updated 11/14/00 Page 157 of 166InvsPolyFunction63422102 2 2 1 ,`

.| + ,`

.| + ,`

.| ++ wx xAwx xAwx xAAy yc c cBrief DescriptionInverse polynomial peak function with center.Sample CurveParametersNumber: 7Names: y0, xc, w, A, A1, A2, A3Meanings: y0 = offset, xc = center, w = width, A = amplitude, A1 = coefficient, A2 = coefficient, A3 =coefficientInitial Values: y0 = 0.0 (vary), xc = 0.0 (vary), w = 1.0 (vary), A = 1.0 (vary), A1 = 0.0 (vary), A2 = 0.0(vary), A3 = 0.0 (vary)Lower Bounds: w > 0.0, A1 0.0, A2 0.0, A3 0.0Upper Bounds: noneScript Accessinvspoly(x,y0,xc,w,A,A1,A2,A3)Function FileFITFUNC\INVSPOLY.FDFLast Updated 11/14/00 Page 158 of 166LorentzFunction( )2 2 042w x xw Ay yc + + Brief DescriptionLorentzian peak function.Sample CurveParametersNumber: 4Names: y0, xc, w, AMeanings: y0 = offset, xc = center, w = width, A = areaInitial Values: y0 = 0.0 (vary), xc = 0.0 (vary), w = 1.0 (vary), A = 1.0 (vary)Lower Bounds: w > 0.0Upper Bounds: noneScript Accesslorentz(x,y0,xc,w,A)Function FileFITFUNC\LORENTZ.FDFLast Updated 11/14/00 Page 159 of 166PearsonVIIFunction( )( ) ( )mucmumu x xw ee muA ymu ]]]

+ 22/ 1) 2 / 1 () 1 2 (1 24 12/ 1Brief DescriptionPearson VII peak function.Sample CurveParametersNumber: 4Names: xc, A, w, muMeanings: xc = center, A = amplitude, w = width, mu = profile shape factorInitial Values: xc = 0.0 (vary), A = 1.0 (vary), w = 1.0 (vary), mu = 1.0 (vary)Lower Bounds: A > 0.0, w > 0.0, mu > 0.0Upper Bounds: noneScript Accesspearsonvii(x,xc,A,w,mu)Function FileFITFUNC\PEARSON7.FDFLast Updated 11/14/00 Page 160 of 166PsdVoigt1Function( ) ( ) ( )]]]]

++ + 222 ln 42 2 02 ln 4142 cx xwucu ewmw x xwm A y y Brief DescriptionPseudo-Voigt peak function type 1.Sample CurveParametersNumber: 5Names: y0, xc, A, w, muMeanings: y0 = offset, xc = center, A = amplitude, w = width, mu = profile shape factorInitial Values: y0 = 0.0 (vary), xc = 0.0 (vary), A = 1.0 (vary), w = 1.0 (vary), mu = 0.5 (vary)Lower Bounds: w > 0.0Upper Bounds: noneScript Accesspsdvoigt1(x,y0,xc,A,w,mu)Function FileFITFUNC\PSDVGT1.FDFLast Updated 11/14/00 Page 161 of 166PsdVoigt2Function( ) ( ) ( )]]]]

++ + 222 ln 42 202 ln 4142 cGx xwGuL cLu ewmw x xwm A y yBrief DescriptionPseudo-Voigt peak function type 2.Sample CurveParametersNumber: 6Names: y0, xc, A, wG, wL, muMeanings: y0 = offset, xc = center, A = amplitude, wG = width, wL = width, mu = profile shape factorInitial 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 > 0.0, wL > 0.0Upper Bounds: noneScript Accesspsdvoigt2(x,y0,xc,A,wG,wL,mu)Function FileFITFUNC\PSDVGT2.FDFLast Updated 11/14/00 Page 162 of 166VoigtFunction

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.| + dttwx xwwewwA y yGcGLtGL2 2 2 2 / 3 02 ln 4 2 ln2 ln 22Brief DescriptionVoigt peak function.Sample CurveParametersNumber: 5Names: y0, xc, A, wG, wLMeanings: y0 = offset, xc = center, A = amplitude, wG = Gaussian width, wL = Lorentzian widthInitial Values: y0 = 0.0 (vary), xc = 0.0 (vary), A = 1.0 (vary), wG = 1.0 (vary), wL = 1.0 (vary)Lower Bounds: wG > 0.0, wL > 0.0Upper Bounds: noneScript Accessvoigt5(x,y0,xc,A,wG,wL)Function FileFITFUNC\VOIGT5.FDFLast Updated 11/14/00 Page 163 of 16612. Waveform FunctionsSine 164SineDamp 165SineSqr 166Last Updated 11/14/00 Page 164 of 166SineFunction

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.| wx xA y c sinBrief DescriptionSine function.Sample CurveParametersNumber: 3Names: xc, w, AMeanings: xc = center, w = width, A = amplitudeInitial Values: xc = 0.0 (vary), w = 1.0 (vary), A = 1.0 (vary)Lower Bounds: w > 0Upper Bounds: noneScript Accesssine(x,xc,w,A)Function FileFITFUNC\SINE.FDFLast Updated 11/14/00 Page 165 of 166SineDampFunction

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.| wx xAe y c tx sin0Brief DescriptionSine damp function.Sample CurveParametersNumber: 4Names: xc, w, t0, AMeanings: xc = center, w = width, t0 = decay constant, A = amplitudeInitial Values: xc = 0.0 (vary), w = 1.0 (vary), t0 = 1.0 (vary), A = 1.0 (vary)Lower Bounds: w > 0.0 , t0 > 0.0Upper Bounds: noneScript Accesssinedamp(x,xc,w,t0,A)Function FileFITFUNC\SINEDAMP.FDFLast Updated 11/14/00 Page 166 of 166SineSqrFunction

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.| wx xA y c2sinBrief DescriptionSine square function.Sample CurveParametersNumber: 3Names: xc, w, AMeanings: xc = center, w = width, A = amplitudeInitial Values: xc = 0.0 (vary), w = 1.0 (vary), A = 1.0 (vary)Lower Bounds: w > 0.0Upper Bounds: noneScript Accesssinesqr(x,xc,w,A)Function FileFITFUNC\SINESQR.FDF