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ZDD - Gen Default - Asymmetric Normal

This is the Zero Distortion Density (ZDD) used in the default GenHVL models. This generalized normal's a₁ center parameter is the mean of the asymmetric peak. The [Z] ZDD is a similar model with a parameterization where a₁ is the center of the underlying normal. The a₃ parameter in the ZDD nomenclature adjusts the third moment or skew.

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

Generalized Default ZDD (One Higher Moment)

a₀ = Area

a₁ = Center (as mean of asymmetric peak)

a₂ = Width (SD of underlying Gaussian)

a₃ = Asymmetry ( fronted -1 > a₃ > 1 tailed)

Built-In Peak Model

  GenNorm[m] (Statistical family)

User-Defined Peaks and View Functions

  GenNorm[m](x,area,mean,width,shape) Asym Generalized Normal Area
  GenNorm[m]_C(x,amplitude,mean,width,shape) Asym Generalized Normal cumulative
  GenNorm[m]_CR(x,amplitude,mean,width,shape) Asym Generalized Normal reverse cumulative