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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.


ZDD - [T]13.PNG

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

C:\1pf2022\Help\home.gif ZDD - [K] ZDD - [V]