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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

a₀ = Area

a₁ = Center

a₂ = Width

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

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

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.