PeakLab v1 Documentation Contents AIST Software Home AIST Software Support

Statistical Functions

Normal (Gaussian)

a_{0} = Area

a_{1} = Center (mean)

a_{2} = Width (SD)

Built in model: Normal

User-defined peaks and view functions: Normal(x,a_{0},a_{1},a_{2})

Normal (Gaussian) Amplitude

a_{0} = Amplitude

a_{1} = Center (mean)

a_{2} = Width (SD)

Built in model: Normal[amp]

User-defined peaks and view functions: Normal[amp](x,a_{0},a_{1},a_{2})

Cauchy (Lorentzian)

a_{0} = Area

a_{1} = Center

a_{2} = Width

Built in model: Cauchy

User-defined peaks and view functions: Cauchy(x,a_{0},a_{1},a_{2})

Cauchy (Lorentzian) Amplitude

a_{0} = Amplitude

a_{1} = Center

a_{2} = Width

Built in model: Cauchy[amp]

User-defined peaks and view functions: Cauchy[amp](x,a_{0},a_{1},a_{2})

Log Normal

a_{0} = Area

a_{1} = Center (¹0)

a_{2} = Width (>0)

Built in model: LogNormal

User-defined peaks and view functions: LogNormal(x,a_{0},a_{1},a_{2})

Log Normal Amplitude

a_{0} = Amplitude

a_{1} = Center (¹0)

a_{2} = Width (>0)

Built in model: LogNormal[amp]

User-defined peaks and view functions: LogNormal[amp](x,a_{0},a_{1},a_{2})

Logistic

a_{0} = Area

a_{1} = Center

a_{2} = Width

Built in model: Logistic

User-defined peaks and view functions: Logistic(x,a_{0},a_{1},a_{2})

Logistic Amplitude

a_{0} = Amplitude

a_{1} = Center

a_{2} = Width

Built in model: Logistic[amp]

User-defined peaks and view functions: Logistic[amp](x,a_{0},a_{1},a_{2})

Laplace (DblSided Exp)

a_{0} = Area

a_{1} = Center

a_{2} = Width

Built in model: Laplace

User-defined peaks and view functions: Laplace(x,a_{0},a_{1},a_{2})

Laplace (DblSided Exp) Amplitude

a_{0} = Amplitude

a_{1} = Center

a_{2} = Width

Built in model: Laplace[amp]

User-defined peaks and view functions: Laplace[amp](x,a_{0},a_{1},a_{2})

Extreme Value

a_{0} = Area

a_{1} = Center

a_{2} = Width (>0)

Built in model: ExtrValue

User-defined peaks and view functions: ExtrValue(x,a_{0},a_{1},a_{2})

Extreme Value Amplitude

a_{0} = Amplitude

a_{1} = Center

a_{2} = Width (>0)

Built in model: ExtrValue[amp]

User-defined peaks and view functions: ExtrValue[amp](x,a_{0},a_{1},a_{2})

Gamma Peak

a_{0} = Area

a_{1} = Center

a_{2} = Width (>0)

a_{3}
= Shape (1.01<a_{3}<167.92)

Built in model: GammaPeak

User-defined peaks and view functions: GammaPeak(x,a_{0},a_{1},a_{2},a_{3})

Gamma Peak Amplitude

a_{0} = Amplitude

a_{1} = Center

a_{2} = Width (>0)

a_{3}
= Shape (1.01<a_{3}<167.92)

Built in model: GammaPeak[amp]

User-defined peaks and view functions: GammaPeak[amp](x,a_{0},a_{1},a_{2},a_{3})

Inverted Gamma Peak

a_{0} = Area

a_{1} = Center

a_{2} = Width (>0)

a_{3}
= Shape (0<a_{3}<167.92)

Built in model: InvGamma

User-defined peaks and view functions: InvGamma(x,a_{0},a_{1},a_{2},a_{3})

Inverted Gamma Peak Amplitude

a_{0} = Amplitude

a_{1} = Center

a_{2} = Width (>0)

a_{3}
= Shape (0<a_{3}<167.92)

Built in model: InvGamma[amp]

User-defined peaks and view functions: InvGamma[amp](x,a_{0},a_{1},a_{2},a_{3})

Weibull

a_{0} = Area

a_{1} = Center

a_{2} = Width (>0)

a_{3}
= Shape (>1.01)

Built in model: Weibull

User-defined peaks and view functions: Weibull(x,a_{0},a_{1},a_{2},a_{3})

Weibull Amplitude

a_{0} = Amplitude

a_{1} = Center

a_{2} = Width (>0)

a_{3}
= Shape (>1.01)

Built in model: Weibull[amp]

User-defined peaks and view functions: Weibull[amp](x,a_{0},a_{1},a_{2},a_{3})

Error

a_{0} = Area

a_{1} = Center

a_{2} = Width (>0)

a_{3}
= Shape (>0)

Built in model: Error

User-defined peaks and view functions: Error(x,a_{0},a_{1},a_{2},a_{3})

Error Amplitude

a_{0} = Amplitude

a_{1} = Center

a_{2} = Width (>0)

a_{3}
= Shape (>0)

Built in model: Error[amp]

User-defined peaks and view functions: Error[amp](x,a_{0},a_{1},a_{2},a_{3})

Chi Squared

a_{0} = Area

a_{1} = Center

a_{2} = Width (>0)

a_{3}
= Shape (2.01<a_{3}<335.84)

Built in model: ChiSq

User-defined peaks and view functions: ChiSq(x,a_{0},a_{1},a_{2},a_{3})

Chi Squared Amplitude

a_{0} = Amplitude

a_{1} = Center

a_{2} = Width (>0)

a_{3}
= Shape (2.01<a_{3}<335.84)

Built in model: ChiSq[amp]

User-defined peaks and view functions: ChiSq[amp](x,a_{0},a_{1},a_{2},a_{3})

Student's t

a_{0} = Area

a_{1} = Center

a_{2} = Width (>0)

a_{3}
= Shape (>0)

Built in model: Student

User-defined peaks and view functions: Student(x,a_{0},a_{1},a_{2},a_{3})

Student's t Amplitude

a_{0} = Amplitude

a_{1} = Center

a_{2} = Width (>0)

a_{3}
= Shape (>0)

Built in model: Student[amp]

User-defined peaks and view functions: Student[amp](x,a_{0},a_{1},a_{2},a_{3})

Beta Peak

a_{0} = Area

a_{1} = Center

a_{2} = Width (>0)

a_{3}
= Shape1 (1.01)

a_{4}
= Shape2 (1.01)

Built in model: BetaPeak

User-defined peaks and view functions: BetaPeak(x,a_{0},a_{1},a_{2},a_{3},a_{4})

Beta Peak Amplitude

a_{0} = Amplitude

a_{1} = Center

a_{2} = Width (>0)

a_{3}
= Shape1 (1.01)

a_{4}
= Shape2 (1.01)

Built in model: BetaPeak[amp]

User-defined peaks and view functions: BetaPeak[amp](x,a_{0},a_{1},a_{2},a_{3},a_{4})

F Variance

a_{0} = Area

a_{1} = Center

a_{2} = Width (>0)

a_{3}
= Shape1 (2<a_{3}<167.92)

a_{4}
= Shape2 (2<a4<167.92)

Built in model: FVariance

User-defined peaks and view functions: FVariance(x,a_{0},a_{1},a_{2},a_{3},a_{4})

FVariance Amplitude

a_{0} = Amplitude

a_{1} = Center

a_{2} = Width (>0)

a_{3}
= Shape1 (2<a_{3}<167.92)

a_{4}
= Shape2 (2<a4<167.92)

Built in model: FVariance[amp]

User-defined peaks and view functions: FVariance[amp](x,a_{0},a_{1},a_{2},a_{3},a_{4})

Pearson VII

a_{0} = Area

a_{1} = Center (mode)

a_{2} = FWHM

a_{3} = Shape
(1=Lorentzian, infinity=Gaussian)

Built in model: PearsonVII

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

Pearson VII (Amplitude)

a_{0} = Amplitude

a_{1} = Center (mode)

a_{2} = FWHM

a_{3} = 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

a_{0} = Area

a_{1} = Center

a_{2} = Width (>0)

a_{3}
= Shape1 (>0)

a_{4}
= Shape2

Built in model: PearsonIV

User-defined peaks and view functions: PearsonIV(x,a_{0},a_{1},a_{2},a_{3},a_{4})

Pearson IV Amplitude

a_{0} = Amplitude

a_{1} = Center

a_{2} = Width (>0)

a_{3}
= Shape1 (>0)

a_{4}
= Shape2

Built in model: PearsonIV[amp]

User-defined peaks and view functions: PearsonIV[amp](x,a_{0},a_{1},a_{2},a_{3},a_{4})

Generalized Normal

a_{0} = Area

a_{1} = Center (median)

a_{2} = Width (>0)

a_{3}
= Asymmetry

Built in model: GenNorm

User-defined peaks and view functions: GenNorm(x,a_{0},a_{1},a_{2},a_{3})

Generalized Normal Amplitude

a_{0} = Amplitude

a_{1} = Center

a_{2} = Width (>0)

a_{3}
= Asymmetry

Built in model: GenNorm[amp]

User-defined peaks and view functions: GenNorm[amp](x,a_{0},a_{1},a_{2},a_{3})

Generalized Normal Alternate Parametrizations

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

a1=mean (Default ZDD)

a_{0} = Area

a_{1} = Center (mean)

a_{2} = Width (>0)

a_{3}
= Asymmetry

Built in model: GenNorm[m]

User-defined peaks and view functions: GenNorm[m](x,a_{0},a_{1},a_{2},a_{3})

a_{1}=mode

a_{0} = Area

a_{1} = Center (mode)

a_{2} = Width (>0)

a_{3}
= Asymmetry

Built in model: GenNorm[c]

User-defined peaks and view functions: GenNorm[c](x,a_{0},a_{1},a_{2},a_{3})

a_{2}=SD

a_{0} = Area

a_{1} = Center (mean)

a_{2} = Width (SD)

a_{3}
= Asymmetry

Built in model: GenNorm[d]

User-defined peaks and view functions: GenNorm[d](x,a_{0},a_{1},a_{2},a_{3})

a_{3}=asym50

a_{0} = Area

a_{1} = Center (mean)

a_{2} = Width (>0)

a_{3}
= Half-Height Asymmetry Asym50

Built in model: GenNorm[a]

User-defined peaks and view functions: GenNorm[a](x,a_{0},a_{1},a_{2},a_{3})

a_{1}=mode, a_{2}=FWHM

a_{0} = Area

a_{1} = Center (mode)

a_{2} = Width (FWHM)

a_{3}
= Asymmetry

Built in model: GenNorm[cw]

User-defined peaks and view functions: GenNorm[cw](x,a_{0},a_{1},a_{2},a_{3})

a_{1}=mean, a_{2}=SD

a_{0} = Area

a_{1} = Center (mean)

a_{2} = Width (SD)

a_{3}
= Asymmetry

Built in model: GenNorm[md]

User-defined peaks and view functions: GenNorm[md](x,a_{0},a_{1},a_{2},a_{3})

a_{1}=mode, a_{2}=SD

a_{0} = Area

a_{1} = Center (mode)

a_{2} = Width (SD)

a_{3}
= Asymmetry

Built in model: GenNorm[cd]

User-defined peaks and view functions: GenNorm[cd](x,a_{0},a_{1},a_{2},a_{3})

a_{1}=mean, a_{2}=variance

a_{0} = Area

a_{1} = Center (mean)

a_{2} = Width (variance)

a_{3}
= Asymmetry

Built in model: GenNorm[mv]

User-defined peaks and view functions: GenNorm[mv](x,a_{0},a_{1},a_{2},a_{3})

a_{1}=mean, a_{2}=variance, a_{3}=skew

a_{0} = Area

a_{1} = Center (mean)

a_{2} = Width (variance)

a_{3}
= Asymmetry (skew)

Built in model: GenNorm[mvs]

User-defined peaks and view functions: GenNorm[mvs](x,a_{0},a_{1},a_{2},a_{3})

a_{1}=mode, a_{2}=FWHM, a_{3}=Asym50

a_{0} = Area

a_{1} = Center (mode)

a_{2} = Half-Height Width (FWHM)

a_{3}
= Half-Height Asymmetry (Asym50)

Built in model: GenNorm[cwa]

User-defined peaks and view functions: GenNorm[cwa](x,a_{0},a_{1},a_{2},a_{3})

a_{1}=mode, a_{3}=Asym50

a_{0} = Area

a_{1} = Center (mode)

a_{2} = Width

a_{3}
= Half-Height Asymmetry (Asym50)

Built in model: GenNorm[ca]

User-defined peaks and view functions: GenNorm[ca](x,a_{0},a_{1},a_{2},a_{3})

Skew Normal

a_{0} = Area

a_{1} = Center

a_{2} = Width

a_{3}
= Asymmetry

Built in model: SkewNormal

User-defined peaks and view functions: SkewNormal(x,a_{0},a_{1},a_{2},a_{3})

GMG (Half-Gaussian Ä Gaussian)

a_{0} = Area

a_{1} = Center

a_{2} = Full-Gaussian Width

a_{3}
= Half-Gaussian Width

Built in model: GMG

User-defined peaks and view functions: GMG(x,a_{0},a_{1},a_{2},a_{3})

EMG (Exponential Ä Gaussian)

a_{0} = Area

a_{1} = Center

a_{2} = Gaussian Width

a_{3}
= Exponential Decay Width (time constant)

Built in model: EMG

User-defined peaks and view functions: EMG(x,a_{0},a_{1},a_{2},a_{3})

EMG Alternate Parametrizations

a_{2}=SD

a_{0} = Area

a_{1} = Center

a_{2} = SD of Convolution

a_{3}
= Exponential Decay Width (time constant)

Built in model: EMG[d]

User-defined peaks and view functions: EMG[d](x,a_{0},a_{1},a_{2},a_{3})

a_{1}=mean, a_{2}=SD

a_{0} = Area

a_{1} = Center (mean)

a_{2} = Width (SD)

a_{3}
= Exponential Decay Width (time constant)

Built in model: EMG[md]

User-defined peaks and view functions: EMG[md](x,a_{0},a_{1},a_{2},a_{3})

NError (Alternate Error Model-Q ZDD)

a_{0} = Area

a_{1} = Center

a_{2} = Width

a_{3}= Error model power (.25 > a_{3} > 4 , Laplace=1, Gaussian=2)

Built in model: NError

User-defined peaks and view functions: NError(x,a_{0},a_{1},a_{2},a_{3})

Extreme Value 4-Parameter

a_{0} = Area

a_{1} = Center

a_{2} = Width (>0)

a_{3 }= Shape (>0)

Built in model: ExtrVal4

User-defined peaks and view functions: ExtrVal4(x,a_{0},a_{1},a_{2},a_{3})

Extreme Value 4-Parameter Amplitude

a_{0} = Amplitude

a_{1} = Center

a_{2} = Width (>0)

a_{3 }= Shape (>0)

Built in model: ExtrVal4[amp]

User-defined peaks and view functions: ExtrVal4[amp](x,a_{0},a_{1},a_{2},a_{3})

Generalized Extreme Value

a_{0} = Area

a_{1} = Center

a_{2} = Width

a_{3}
= Shape

Built in model: GenExtrVal

User-defined peaks and view functions: GenExtrVal(x,a_{0},a_{1},a_{2},a_{3})

Generalized Extreme Value Amplitude

a_{0} = Amplitude

a_{1} = Center

a_{2} = Width

a_{3}
= Shape

Built in model: GenExtrVal[amp]

User-defined peaks and view functions: GenExtrVal[amp](x,a_{0},a_{1},a_{2},a_{3})

Generalized Logistic

a_{0} = Area

a_{1} = Center

a_{2} = Width

a_{3}
= Shape

Built in model: GenLogistic

User-defined peaks and view functions:GenLogistic(x,a_{0},a_{1},a_{2},a_{3})

Generalized Logistic Amplitude

a_{0} = Amplitude

a_{1} = Center

a_{2} = Width

a_{3}
= Shape

Built in model: GenLogistic[amp]

User-defined peaks and view functions: GenLogistic[amp](x,a_{0},a_{1},a_{2},a_{3})

Generalized Error

a_{0} = Area

a_{1} = Center

a_{2} = Width

a_{3}
= Power of Tail Decay

a_{4}
= Asymmetry

Built in model: GenError

User-defined peaks and view functions: GenError(x,a_{0},a_{1},a_{2},a_{3},a_{4})

Generalized Error, Two-Width

a_{0} = Area

a_{1} = Center

a_{2} = Width, right

a_{3} = Fraction of a_{2} for Width, left

a_{4} = Error model power (.25 > a_{4}
> 4 , Laplace=1, Gaussian=2)

a_{5}
= Asymmetry ( fronted -1 > a_{5}
> 1 tailed)

Built in model: GenError2

User-defined peaks and view functions: GenError2(x,a_{0},a_{1},a_{2},a_{3},a_{4})

Generalized Student's t

a_{0} = Area

a_{1} = Center

a_{2} = Width

a_{3}
= Tailing (Student's t nu or DOF)

a_{4}
= Asymmetry

Built in model: GenStudent

User-defined peaks and view functions: GenStudent(x,a_{0},a_{1},a_{2},a_{3},a_{4})

SDS (Symmetric Double Sigmoid)

a_{0} = Area

a_{1} = Center

a_{2} = Width

a_{3}
= Sigmoid Width

Built in model: SDS

User-defined peaks and view functions: SDS(x,a_{0},a_{1},a_{2},a_{3})

SDS (Symmetric Double Sigmoid) Amplitude

a_{0} = Amplitude

a_{1} = Center

a_{2} = Width

a_{3}
= Sigmoid Width

Built in model: SDS[amp]

User-defined peaks and view functions: SDS[amp](x,a_{0},a_{1},a_{2},a_{3})

Generalized SDS (Symmetric Double Sigmoid)

a_{0} = Area

a_{1} = Center

a_{2} = Width

a_{3}
= Adjusted Sigmoid Width (approximates Gaussian width in Generalized Models)

a_{4}
= Asymmetry

Built in model: GenSDS

User-defined peaks and view functions: GenSDS(x,a_{0},a_{1},a_{2},a_{3},a_{4})

Generalized GMG (Half-Gaussian Modified Gaussian)

a_{0} = Area

a_{1} = Center

a_{2} = Width (>0)

a_{3}= Half-Gaussian convolution width (>0)

a_{4} = Asymmetry ( fronted -1 > a_{4} > 1 tailed)

Built in model: GenGMG

User-defined peaks and view functions: GenGMG(x,a_{0},a_{1},a_{2},a_{3},a_{4})