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ZDD - [T] Generalized Student's t (Asymmetric)

This is the Zero Distortion Density (ZDD) used in the GenHVL[T] models. The [T] model is a further generalization of the [S] ZDD. The a₃ parameter (as in the [S] model) adjusts the nu or DOF of the Student's t, altering the fourth moment or kurtosis of the peak. The a₄ parameter in the ZDD nomenclature below adjusts the asymmetry, and thus the third moment or skew of the peak.

This is also the ZDD used in the GenNLC[T] models. For the GenNLC[T] 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.

[T] ZDD

a₀ = Area

a₁ = Center

a₂ = Width

a₃= DOF or nu (1>a₃>1000000, Gaussian nu=Infinity, Lorentzian nu=1)

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

Built-In Peak Model

  GenStudent (Statistical family)

User-Defined Peaks and View Functions

  GenStudent(x,area,center,width,s-nu,z-asym) Generalized Student's t Area
  GenStudent_C(x,amplitude,center,width,s-nu) Gen. Student's t cumulative
  GenStudent_CR(x,amplitude,center,width,s-nu) Gen. Student's t reverse cumulative