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ZDD - [Yp2] Generalized Error 2-Width (Overload Shapes)

This is the Zero Distortion Density (ZDD) used in the GenHVL[Yp2] models.

This is the [Yp2] ZDD is the [Y] ZDD modified to have both a left and right side width. This model is used only for preparative (overload) shapes. The starting estimates for the [Yp2] density assume such shapes.

This generalized error a₁ center parameter is the mean of the underlying Normal. The a₄ parameter in the ZDD nomenclature below adjusts the power of the decay, and thus the fourth moment or kurtosis of the peak. The a₅ parameter in the ZDD nomenclature adjusts the asymmetry, and thus the third moment or skew of the peak.

There is no GenNLC[Yp2] model.

[Yp2] ZDD

a₀ = Area

a₁ = Center

a₂ = Width

a₃ = Width Asymmetry (right side width)/(left side width)
a₄ = Error model power (.25 > a₄ > 4 , Laplace=1, Gaussian=2)
a₅ = Statistical Asymmetry ( fronted -1 > a₅ > 1 tailed)

For these plots, a power of decay of 1.2 is used (a value for a partial overload envelope). In the first set of peaks the width asymmetry a₃ is varied from 1 to 100, the peaks changing from a symmetric to very nearly a right triangular peak. In the second set of peaks, the statistical asymmetry a₄ increases in negative values, sharply drawing in (thinning) the tail. In the last set of peaks, the statistical asymmetry a₄ increases in positive values, drawing outward (fattening) the tail. These are the behaviors in a ZDD needed to fit envelope overload shapes. The [Yp2] ZDD is needed for partial overload shapes. The simpler power of 1 [Yp2E] ZDD can be used for full envelope overload shapes.

Built-In Peak Model

  GenError2 (Statistical family)

User-Defined Peaks and View Functions

  GenError2(x,area,center,Lwidth,Rfraction,n-power,z-asym) Generalized Error 2-width Area
  GenError2_C(x,amplitude,center,Lwidth,Rfraction,n-power,z-asym) Gen. Error 2-width cumulative
  GenError2_CR(x,amplitude,center,Lwidth,Rfraction,n-power,z-asym) Gen. Error 2-width reverse cumulative

This Asymmetric Error Model with 2-widths is part of the unique content in the product covered by its copyright.