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ZDD - [Y] Generalized Error Model


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

The [Y] model is used for analytic peak shapes and the [Yp] model is used only for preparative (extremely high overload) shapes. The models are identical, but the assumptions made for starting estimates are sharply different.

This generalized normal's a1 center parameter is the mean of the underlying Normal. The [Y] model is a further generalization of the [Z] ZDD. The a3 parameter in the ZDD nomenclature below adjusts the power of the decay, and thus the fourth moment or kurtosis of the peak. The a4 parameter in the ZDD nomenclature adjusts the asymmetry, and thus the third moment or skew of the peak.

This is also the ZDD used in the GenNLC[Y] models. For the GenNLC[Y] models, a0, a1, and a3 will be identical. The a2 width or second moment term will reflect a kinetic time constant, and a4 will reflect an NLC asymmetry normalized to 0.5 for the Giddings ZDD. Please see the GenHVL and GenNLC equivalence topic for further details.

[Y] ZDD

 

ZDD - [Y]13.png

a0 = Area

a1 = Center

a2 = Width

a3= Error model power (.25 > a3 > 4 , Laplace=1, Gaussian=2)

a4 = Asymmetry ( fronted -1 > a4 > 1 tailed)

v5_ZDD_[Y].png

In this graph, the outer peaks vary the asymmetry a4 at positive and negative values. The peaks in the center of the plot vary the a3 tailing at a fixed positive and negative asymmetry.

Built-In Peak Model

  GenError (Statistical family)

User-Defined Peaks and View Functions

  GenError(x,area,center,width,n-power,z-asym) Generalized Error Area
  GenError_C(x,amplitude,center,width,n-power,z-asym) Gen. Error cumulative
  GenError_CR(x,amplitude,center,width,n-power,z-asym) Gen. Error reverse cumulative

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



c:\1pf\v5 help\home.gif ZDD - [Z] ZDD - [Q]