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ZDD - Giddings

This is the Zero Distortion Density (ZDD) inferred in all GenNLC models. This generalized normal's a₁ center parameter is the mean or centroid of the Giddings density. The a₂ is a dimensionless time constant which represents the lumped contributions to all band broadening that can be described by first order kinetics.

Peak

Cumulative

Reverse Cumulative

a₀ = Area

a₁ = Center (as mean of underlying Gaussian)

a₂ = Width (as time constant)

The Giddings ZDD uses the above approximations. Modified Bessel functions and modified Bessel function integrals are not used.

Built-In Peak Model

  Gidx (Statistical family) Approximation
  Giddings (Chromatography family) Full-Precision

User-Defined Peaks and View Functions

  Gidx(x,area,mean,Gidwidth) Giddings (Approximation)
  Giddings(x,area,center,width) Giddings (Full-Precision)

  Gidx_C(x,area,mean,Gidwidth) Giddings (Approximation) cumulative
  Gidx_CR(x,area,mean,Gidwidth) Giddings (Approximation) reverse cumulative

To use the full precision Giddings cumulatives and reverse cumulative, you will need the Bessel function integral:
  TFn(u,v) Modified Bessel Integral for NLC, Giddings CDF complement (u=a₁/a₂,v=x/a₂)

This Giddings approximation is part of the unique content in the product covered by its copyright.