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
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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 ]]]
,`
.|
,`
.| +]]]
,`
.|
,`
.| ++ + 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
,`
.| + 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
,`
.| 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
,`
.|+
,`
.| + 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( ) ( )( )''
,`
.| + ++ + ++ 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
,`
.|+ 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
,`
.|+ 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
,`
.| + 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
,`
.|+++ + 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 ]]]
,`
.|
,`
.| +]]]
,`
.|
,`
.| ++ + 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( ) ( )( )''
,`
.| + ++ + ++ 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]]]
+ ,`
.| ]]]
,`
.| + 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
,`
.|+ 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
,`
.|+ 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
,`
.| + ,`
.| + ,`
.| ++ 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
,`
.|++ 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
,`
.|+
,`
.| + 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[ ] [ ]
,`
.| +
,`
.| +
,`
.| +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
,`
.|+++ + 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
,`
.|+
,`
.| + 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
,`
.| 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
,`
.| 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
,`
.| 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