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ZDD - [Yp2E] Generalized Laplace 2-Width (High Overload Shapes)

This is the Zero Distortion Density (ZDD) used in the GenHVL[Yp2E] models.

The [Yp2E] ZDD is the [Yp2] ZDD with a fixed power of decay of 1, an exponential decay. This model is used only for preparative (extremely high overload) shapes. The starting estimates for the [Yp2E] density assume such shapes.

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

There is no GenNLC[Yp2E] model.

[Yp2E] ZDD

a₀ = Area

a₁ = Center

a₂ = Width

a₃ = Width Asymmetry (right side width)/(left side width)
a₄ = Statistical Asymmetry ( fronted -1 > a₄ > 1 tailed)

In the first set of peaks the width asymmetry a₃ is varied from 1 to 100, the peaks changing from a double-exponential or Laplace 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 full envelope overload shapes.

Built-In Peak Model

  GenLaplace2 (Statistical family)

User-Defined Peaks and View Functions

  GenLaplace2(x,area,center,width,n-power,z-asym) Generalized Error Area
  GenLaplace2_C(x,amplitude,center,width,n-power,z-asym) Gen. Error cumulative
  GenLaplace2_CR(x,amplitude,center,width,n-power,z-asym) Gen. Error reverse cumulative

This Generalized Laplace Model is part of the unique content in the product covered by its copyright.