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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

 

ZDD - [YP2]3.PNG

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)
a
5 = Statistical Asymmetry ( fronted -1 > a5 > 1 tailed)

v5_ZDD_[Yp2].png

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.



C:\1pf2022\Help\home.gif ZDD - [YpE] ZDD - [Yp2E]