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Statistical Functions

Normal (Gaussian)

a0 = Area

a1 = Center (mean)

a2 = Width (SD)

Built in model: Normal

User-defined peaks and view functions: Normal(x,a0,a1,a2)

Normal (Gaussian) Amplitude

a0 = Amplitude

a1 = Center (mean)

a2 = Width (SD)

Built in model: Normal[amp]

User-defined peaks and view functions: Normal[amp](x,a0,a1,a2)

Cauchy (Lorentzian)

a0 = Area

a1 = Center

a2 = Width

Built in model: Cauchy

User-defined peaks and view functions: Cauchy(x,a0,a1,a2)

Cauchy (Lorentzian) Amplitude

a0 = Amplitude

a1 = Center

a2 = Width

Built in model: Cauchy[amp]

User-defined peaks and view functions: Cauchy[amp](x,a0,a1,a2)

Log Normal

a0 = Area

a1 = Center (¹0)

a2 = Width (>0)

Built in model: LogNormal

User-defined peaks and view functions: LogNormal(x,a0,a1,a2)

Log Normal Amplitude

a0 = Amplitude

a1 = Center (¹0)

a2 = Width (>0)

Built in model: LogNormal[amp]

User-defined peaks and view functions: LogNormal[amp](x,a0,a1,a2)

Logistic

a0 = Area

a1 = Center

a2 = Width

Built in model: Logistic

User-defined peaks and view functions: Logistic(x,a0,a1,a2)

Logistic Amplitude

a0 = Amplitude

a1 = Center

a2 = Width

Built in model: Logistic[amp]

User-defined peaks and view functions: Logistic[amp](x,a0,a1,a2)

Laplace (DblSided Exp)

a0 = Area

a1 = Center

a2 = Width

Built in model: Laplace

User-defined peaks and view functions: Laplace(x,a0,a1,a2)

Laplace (DblSided Exp) Amplitude

a0 = Amplitude

a1 = Center

a2 = Width

Built in model: Laplace[amp]

User-defined peaks and view functions: Laplace[amp](x,a0,a1,a2)

Extreme Value

a0 = Area

a1 = Center

a2 = Width (>0)

Built in model: ExtrValue

User-defined peaks and view functions: ExtrValue(x,a0,a1,a2)

Extreme Value Amplitude

a0 = Amplitude

a1 = Center

a2 = Width (>0)

Built in model: ExtrValue[amp]

User-defined peaks and view functions: ExtrValue[amp](x,a0,a1,a2)

Gamma Peak

a0 = Area

a1 = Center

a2 = Width (>0)

a3 = Shape (1.01<a3<167.92)

Built in model: GammaPeak

User-defined peaks and view functions: GammaPeak(x,a0,a1,a2,a3)

Gamma Peak Amplitude

a0 = Amplitude

a1 = Center

a2 = Width (>0)

a3 = Shape (1.01<a3<167.92)

Built in model: GammaPeak[amp]

User-defined peaks and view functions: GammaPeak[amp](x,a0,a1,a2,a3)

Inverted Gamma Peak

a0 = Area

a1 = Center

a2 = Width (>0)

a3 = Shape (0<a3<167.92)

Built in model: InvGamma

User-defined peaks and view functions: InvGamma(x,a0,a1,a2,a3)

Inverted Gamma Peak Amplitude

a0 = Amplitude

a1 = Center

a2 = Width (>0)

a3 = Shape (0<a3<167.92)

Built in model: InvGamma[amp]

User-defined peaks and view functions: InvGamma[amp](x,a0,a1,a2,a3)

Weibull

a0 = Area

a1 = Center

a2 = Width (>0)

a3 = Shape (>1.01)

Built in model: Weibull

User-defined peaks and view functions: Weibull(x,a0,a1,a2,a3)

Weibull Amplitude

a0 = Amplitude

a1 = Center

a2 = Width (>0)

a3 = Shape (>1.01)

Built in model: Weibull[amp]

User-defined peaks and view functions: Weibull[amp](x,a0,a1,a2,a3)

Error

a0 = Area

a1 = Center

a2 = Width (>0)

a3 = Shape (>0)

Built in model: Error

User-defined peaks and view functions: Error(x,a0,a1,a2,a3)

Error Amplitude

a0 = Amplitude

a1 = Center

a2 = Width (>0)

a3 = Shape (>0)

Built in model: Error[amp]

User-defined peaks and view functions: Error[amp](x,a0,a1,a2,a3)

Chi Squared

a0 = Area

a1 = Center

a2 = Width (>0)

a3 = Shape (2.01<a3<335.84)

Built in model: ChiSq

User-defined peaks and view functions: ChiSq(x,a0,a1,a2,a3)

Chi Squared Amplitude

a0 = Amplitude

a1 = Center

a2 = Width (>0)

a3 = Shape (2.01<a3<335.84)

Built in model: ChiSq[amp]

User-defined peaks and view functions: ChiSq[amp](x,a0,a1,a2,a3)

Student's t

a0 = Area

a1 = Center

a2 = Width (>0)

a3 = Shape (>0)

Built in model: Student

User-defined peaks and view functions: Student(x,a0,a1,a2,a3)

Student's t Amplitude

a0 = Amplitude

a1 = Center

a2 = Width (>0)

a3 = Shape (>0)

Built in model: Student[amp]

User-defined peaks and view functions: Student[amp](x,a0,a1,a2,a3)

Beta Peak

a0 = Area

a1 = Center

a2 = Width (>0)

a3 = Shape1 (1.01)

a4 = Shape2 (1.01)

Built in model: BetaPeak

User-defined peaks and view functions: BetaPeak(x,a0,a1,a2,a3,a4)

Beta Peak Amplitude

a0 = Amplitude

a1 = Center

a2 = Width (>0)

a3 = Shape1 (1.01)

a4 = Shape2 (1.01)

Built in model: BetaPeak[amp]

User-defined peaks and view functions: BetaPeak[amp](x,a0,a1,a2,a3,a4)

F Variance

a0 = Area

a1 = Center

a2 = Width (>0)

a3 = Shape1 (2<a3<167.92)

a4 = Shape2 (2<a4<167.92)

Built in model: FVariance

User-defined peaks and view functions: FVariance(x,a0,a1,a2,a3,a4)

FVariance Amplitude

a0 = Amplitude

a1 = Center

a2 = Width (>0)

a3 = Shape1 (2<a3<167.92)

a4 = Shape2 (2<a4<167.92)

Built in model: FVariance[amp]

User-defined peaks and view functions: FVariance[amp](x,a0,a1,a2,a3,a4)

Pearson VII

a0 = Area

a1 = Center (mode)

a2 = FWHM

a3 = Shape (1=Lorentzian, infinity=Gaussian)

Built in model: PearsonVII

User-defined peaks and view functions: PearsonVII(x,a0,a1,a2,a3)

Pearson VII (Amplitude)

a0 = Amplitude

a1 = Center (mode)

a2 = FWHM

a3 = Shape (1=Lorentzian, infinity=Gaussian)

Built in model:PearsonVII[amp]

User-defined peaks and view functions: PearsonVII[amp](x,a0,a1,a2,a3)

Pearson IV

a0 = Area

a1 = Center

a2 = Width (>0)

a3 = Shape1 (>0)

a4 = Shape2

Built in model: PearsonIV

User-defined peaks and view functions: PearsonIV(x,a0,a1,a2,a3,a4)

Pearson IV Amplitude

a0 = Amplitude

a1 = Center

a2 = Width (>0)

a3 = Shape1 (>0)

a4 = Shape2

Built in model: PearsonIV[amp]

User-defined peaks and view functions: PearsonIV[amp](x,a0,a1,a2,a3,a4)

Generalized Normal

a0 = Area

a1 = Center (median)

a2 = Width (>0)

a3 = Asymmetry

Built in model: GenNorm

User-defined peaks and view functions: GenNorm(x,a0,a1,a2,a3)

Generalized Normal Amplitude

a0 = Amplitude

a1 = Center

a2 = Width (>0)

a3 = Asymmetry

Built in model: GenNorm[amp]

User-defined peaks and view functions: GenNorm[amp](x,a0,a1,a2,a3)

Generalized Normal Alternate Parametrizations

The Asymmetric Generalized Normal is available in a number of different parametrizations.

a1=mean (Default ZDD)

a0 = Area

a1 = Center (mean)

a2 = Width (>0)

a3 = Asymmetry

Built in model: GenNorm[m]

User-defined peaks and view functions: GenNorm[m](x,a0,a1,a2,a3)

a1=mode

a0 = Area

a1 = Center (mode)

a2 = Width (>0)

a3 = Asymmetry

Built in model: GenNorm[c]

User-defined peaks and view functions: GenNorm[c](x,a0,a1,a2,a3)

a2=SD

a0 = Area

a1 = Center (mean)

a2 = Width (SD)

a3 = Asymmetry

Built in model: GenNorm[d]

User-defined peaks and view functions: GenNorm[d](x,a0,a1,a2,a3)

a3=asym50

a0 = Area

a1 = Center (mean)

a2 = Width (>0)

a3 = Half-Height Asymmetry Asym50

Built in model: GenNorm[a]

User-defined peaks and view functions: GenNorm[a](x,a0,a1,a2,a3)

a1=mode, a2=FWHM

a0 = Area

a1 = Center (mode)

a2 = Width (FWHM)

a3 = Asymmetry

Built in model: GenNorm[cw]

User-defined peaks and view functions: GenNorm[cw](x,a0,a1,a2,a3)

a1=mean, a2=SD

a0 = Area

a1 = Center (mean)

a2 = Width (SD)

a3 = Asymmetry

Built in model: GenNorm[md]

User-defined peaks and view functions: GenNorm[md](x,a0,a1,a2,a3)

a1=mode, a2=SD

a0 = Area

a1 = Center (mode)

a2 = Width (SD)

a3 = Asymmetry

Built in model: GenNorm[cd]

User-defined peaks and view functions: GenNorm[cd](x,a0,a1,a2,a3)

a1=mean, a2=variance

a0 = Area

a1 = Center (mean)

a2 = Width (variance)

a3 = Asymmetry

Built in model: GenNorm[mv]

User-defined peaks and view functions: GenNorm[mv](x,a0,a1,a2,a3)

a1=mean, a2=variance, a3=skew

a0 = Area

a1 = Center (mean)

a2 = Width (variance)

a3 = Asymmetry (skew)

Built in model: GenNorm[mvs]

User-defined peaks and view functions: GenNorm[mvs](x,a0,a1,a2,a3)

a1=mode, a2=FWHM, a3=Asym50

a0 = Area

a1 = Center (mode)

a2 = Half-Height Width (FWHM)

a3 = Half-Height Asymmetry (Asym50)

Built in model: GenNorm[cwa]

User-defined peaks and view functions: GenNorm[cwa](x,a0,a1,a2,a3)

a1=mode, a3=Asym50

a0 = Area

a1 = Center (mode)

a2 = Width

a3 = Half-Height Asymmetry (Asym50)

Built in model: GenNorm[ca]

User-defined peaks and view functions: GenNorm[ca](x,a0,a1,a2,a3)

Skew Normal

a0 = Area

a1 = Center

a2 = Width

a3 = Asymmetry

Built in model: SkewNormal

User-defined peaks and view functions: SkewNormal(x,a0,a1,a2,a3)

GMG (Half-Gaussian Ä Gaussian)

a0 = Area

a1 = Center

a2 = Full-Gaussian Width

a3 = Half-Gaussian Width

Built in model: GMG

User-defined peaks and view functions: GMG(x,a0,a1,a2,a3)

EMG (Exponential Ä Gaussian)

a0 = Area

a1 = Center

a2 = Gaussian Width

a3 = Exponential Decay Width (time constant)

Built in model: EMG

User-defined peaks and view functions: EMG(x,a0,a1,a2,a3)

EMG Alternate Parametrizations

a2=SD

a0 = Area

a1 = Center

a2 = SD of Convolution

a3 = Exponential Decay Width (time constant)

Built in model: EMG[d]

User-defined peaks and view functions: EMG[d](x,a0,a1,a2,a3)

a1=mean, a2=SD

a0 = Area

a1 = Center (mean)

a2 = Width (SD)

a3 = Exponential Decay Width (time constant)

Built in model: EMG[md]

User-defined peaks and view functions: EMG[md](x,a0,a1,a2,a3)

NError (Alternate Error Model-Q ZDD)

a0 = Area

a1 = Center

a2 = Width

a3= Error model power (.25 > a3 > 4 , Laplace=1, Gaussian=2)

Built in model: NError

User-defined peaks and view functions: NError(x,a0,a1,a2,a3)

Extreme Value 4-Parameter

a0 = Area

a1 = Center

a2 = Width (>0)

a3 = Shape (>0)

Built in model: ExtrVal4

User-defined peaks and view functions: ExtrVal4(x,a0,a1,a2,a3)

Extreme Value 4-Parameter Amplitude

a0 = Amplitude

a1 = Center

a2 = Width (>0)

a3 = Shape (>0)

Built in model: ExtrVal4[amp]

User-defined peaks and view functions: ExtrVal4[amp](x,a0,a1,a2,a3)

Generalized Extreme Value

a0 = Area

a1 = Center

a2 = Width

a3 = Shape

Built in model: GenExtrVal

User-defined peaks and view functions: GenExtrVal(x,a0,a1,a2,a3)

Generalized Extreme Value Amplitude

a0 = Amplitude

a1 = Center

a2 = Width

a3 = Shape

Built in model: GenExtrVal[amp]

User-defined peaks and view functions: GenExtrVal[amp](x,a0,a1,a2,a3)

Generalized Logistic

a0 = Area

a1 = Center

a2 = Width

a3 = Shape

Built in model: GenLogistic

User-defined peaks and view functions:GenLogistic(x,a0,a1,a2,a3)

Generalized Logistic Amplitude

a0 = Amplitude

a1 = Center

a2 = Width

a3 = Shape

Built in model: GenLogistic[amp]

User-defined peaks and view functions: GenLogistic[amp](x,a0,a1,a2,a3)

Generalized Error

a0 = Area

a1 = Center

a2 = Width

a3 = Power of Tail Decay

a4 = Asymmetry

Built in model: GenError

User-defined peaks and view functions: GenError(x,a0,a1,a2,a3,a4)

Generalized Error, Two-Width

a0 = Area

a1 = Center

a2 = Width, right
a3 = Fraction of a2 for Width, left
a4 = Error model power (.25 > a4 > 4 , Laplace=1, Gaussian=2)

a5 = Asymmetry ( fronted -1 > a5 > 1 tailed)

Built in model: GenError2

User-defined peaks and view functions: GenError2(x,a0,a1,a2,a3,a4)

Generalized Student's t

a0 = Area

a1 = Center

a2 = Width

a3 = Tailing (Student's t nu or DOF)

a4 = Asymmetry

Built in model: GenStudent

User-defined peaks and view functions: GenStudent(x,a0,a1,a2,a3,a4)

SDS (Symmetric Double Sigmoid)

a0 = Area

a1 = Center

a2 = Width

a3 = Sigmoid Width

Built in model: SDS

User-defined peaks and view functions: SDS(x,a0,a1,a2,a3)

SDS (Symmetric Double Sigmoid) Amplitude

a0 = Amplitude

a1 = Center

a2 = Width

a3 = Sigmoid Width

Built in model: SDS[amp]

User-defined peaks and view functions: SDS[amp](x,a0,a1,a2,a3)

Generalized SDS (Symmetric Double Sigmoid)

a0 = Area

a1 = Center

a2 = Width

a3 = Adjusted Sigmoid Width (approximates Gaussian width in Generalized Models)

a4 = Asymmetry

Built in model: GenSDS

User-defined peaks and view functions: GenSDS(x,a0,a1,a2,a3,a4)

Generalized GMG (Half-Gaussian Modified Gaussian)

a0 = Area

a1 = Center

a2 = Width (>0)

a3= Half-Gaussian convolution width (>0)

a4 = Asymmetry ( fronted -1 > a4 > 1 tailed)

Built in model: GenGMG

User-defined peaks and view functions: GenGMG(x,a0,a1,a2,a3,a4)