PeakLab v1 Documentation Contents            AIST Software Home            AIST Software Support

Generalized HVL Models

The Generalized HVL Model Template

The generalized Haarhoff VanderLinde (HVL) models use the basic HVL (one term slope of adsorption isotherm) in the following template:

a₀ = area of the overall model

a₁ = the center value used in the density and cumulatives

a₂ = the width value used in the density and cumulatives

a₃ = HVL chromatographic distortion parameter (fronted for a₃<0, tailed for a₃>0)

Density = PDF for the specified ZDD (zero distortion density), area=1

Cumulative = CDF for the specified ZDD, magnitude=1

RevCumulative = CDF complement for the ZDD, magnitude=1

The a₃ distortion only appears in the the template and nowhere in the density and cumulative terms.

For user-defined peak models, the MHVL(a0,a1,a2,a3,Density,Cumulative,RevCumulative) built-in function implements the above template.

Parameter Description

In general, the following applies:

a₀ = the area or zeroth moment parameter

a₁ = parameter related to first moment, the center value (this will be model specific)

a₂ = parameter related to the square root of the second moment, the width value (this will be model specific)

a₃ = the HVL chromatographic distortion parameter (fronted for a₃<0, tailed for a₃>0) (identical across all GenHVL models)

a₄ = for 5 parameter models, the parameter relating to the skew or third moment; for 6 parameter models, the parameter relating to the kurtosis or fourth moment

a₅ = for 6 parameter models, the parameter relating to the skew or third moment

The Generalized HVL Models

HVL (Full Range)

GenHVL - Generalized Normal ZDD

Gen2HVL - Generalized Error Model ZDD

GenHVL[Z] - [Z] Generalized Normal ZDD

GenHVL[Y] - [Y] Generalized Error Model ZDD

GenHVL[G] - [G] Half-Gaussian Modified Gaussian (GMG)

GenHVL[E] - [E] Exponentially-Modified Gaussian (EMG)

GenHVL[Q] - [Q] Error Model (Symmetric)

GenHVL[S] - [S] Student's t (Symmetric)

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

GenHVL[V] - [V] Generalized GMG

GenHVL[Yp] - [Yp] Asymmetric Error Model (High Overload Shapes Only)

GenHVL[YpE] - [YpE] Generalized Laplace (High Overload Shapes Only)
GenHVL[Yp2] - [Yp2] Asymmetric Error Model Two-Width (High Overload Shapes Only)

GenHVL[Yp2E] - [Yp2E] Generalized Laplace Two-Width (High Overload Shapes Only)

GenHVL[K] - [K] Generalized Two-Sided Kinetic Orders 0,1 (High Overload Shapes Only)

GenHVL[W] - [W] Generalized Error Model, Linear Gradient (Gradient HPLC Only)