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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.