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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 a_{1} center parameter is the mean of the underlying Normal. The [Y]
model is a further generalization of the [Z] ZDD. The a_{3} parameter in the ZDD nomenclature
below adjusts the power of the decay, and thus the fourth moment or kurtosis
of the peak. The a_{4}
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, a_{0}, a_{1},
and a_{3} will be identical. The a_{2}
width or second moment term will reflect a kinetic time constant, and a_{4}
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

a_{0} = Area

a_{1} = Center

a_{2} = Width

a_{3}= Error model power (.25 > a_{3} > 4 , Laplace=1, Gaussian=2)

a_{4} = Asymmetry
( fronted -1 > a_{4} > 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.