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GenHVL[YpE] - [YpE] Generalized Laplace ZDD

The GenHVL[YpE] model is specialization of the GenHVL[Yp] model. The [YpE] ZDD allows the skew, the third moment, to vary and the kurtosis, the fourth moment or 'fatness' of the tails, is fixed at the decay of an exponential. The GenHVL[YpE] model is a simplification for fitting highly overloaded preparative peak shapes.

By inserting the [YpE] Generalized Laplace or Double-Sided Exponential ZDD for the PDF, CDF, and CDFc in GenHVL template, we produce the GenHVL[YpE] model:

a0 = Area

a1 = Center (as mean of underlying normal ZDD)

a2 = Width (SD of underlying normal ZDD)

a3 = HVL Chromatographic distortion ( -1 > a3 > 1 )

a4 = ZDD asymmetry ( -1 > a4 > 1 ), adjusts skew (third moment)

Built in model: GenHVL[YpE]

User-defined peaks and view functions: GenHVL[YpE](x,a0,a1,a2,a3,a4)

Using the GenHVL[YpE] for Preparative Peaks

When an overload is especially high, a double-sided exponential ZDD in the GenHVL template produces real-world overload shapes. Using the GenHVL[YpE] model is the same as using the GenHVL[Yp] with its a4 locked at 1.0. In the GenHVL[YpE] the a4 asymmetry mainly controls the shape of the envelope as in the plot below.

GenHVL[YpE] Considerations

The GenHVL[YpE] model is the GenHVL[Y] model with a starting estimate algorithm designed for high overload shapes and the power of decay parameter locked at 1.0, a double exponential or Laplace. You will need to use the the GenHVL[Yp] model for moderate overloads where this Laplace ZDD assumption is invalid. The GenHVL[Yp] will adjust between the Gaussian and the Laplace decay.

The GenHVL[YpE] model is much faster than the GenHVL[Yp] and may be more robust when fitting very high overload shapes.

When fitting overload peaks, we have no experience with whether or not the a4 parameter can be assumed constant (shared) across multiple solutes.

The GenHVL[YpE]<irf> composite fits, the model with a convolution integral describing the instrumental distortions, isolate the intrinsic chromatographic distortion from the IRF instrumental distortion only when the data are of a sufficient S/N and quality to realize two independent deconvolutions within the fitting. For noisy samples, you will probably have to remove the IRF prior using independent determinations of the IRF parameters.

If there are multiple peaks, the a2 and a3 will probably be varied (independently fitted) for each peak.

The GenHVL[YpE] model is part of the unique content in the product covered by its copyright.