PeakLab v1 Documentation Contents AIST Software Home AIST Software Support

ZDD - [Yp2] Generalized Error 2-Width (Overload Shapes)

This is the Zero Distortion Density (ZDD) used in the GenHVL[Yp2] models.

This is the [Yp2] ZDD is the [Y] ZDD modified to have both a left and right side width. This model is used only for preparative (overload) shapes. The starting estimates for the [Yp2] density assume such shapes.

This generalized error a_{1} center parameter is the mean of the underlying Normal. The a_{4}
parameter in the ZDD nomenclature below adjusts the power of the decay, and thus the fourth moment or
kurtosis of the peak. The a_{5}
parameter in the ZDD nomenclature adjusts the asymmetry, and thus the third moment or skew of the peak.

There is no GenNLC[Yp2] model.

[Yp2] ZDD

a_{0} = Area

a_{1} = Center

a_{2} = Width

a_{3} = Width Asymmetry (right side width)/(left side width)

a_{4} = Error model power (.25 > a_{4}
> 4 , Laplace=1, Gaussian=2)

a_{5} =
Statistical Asymmetry ( fronted -1 > a_{5}
> 1 tailed)

For these plots, a power of decay of 1.2 is used (a value for a partial
overload envelope). In the first set of peaks the width asymmetry a_{3}
is varied from 1 to 100, the peaks changing from a symmetric to very nearly a right triangular peak. In
the second set of peaks, the statistical asymmetry a_{4}
increases in negative values, sharply drawing in (thinning) the tail. In the last set of peaks, the statistical
asymmetry a_{4} increases in positive values, drawing
outward (fattening) the tail. These are the behaviors in a ZDD needed to fit envelope overload shapes.
The [Yp2] ZDD is needed for partial overload shapes. The simpler power of 1 [Yp2E]
ZDD can be used for full envelope overload shapes.

Built-In Peak Model

GenError2 (Statistical family)

User-Defined Peaks and View Functions

GenError2(x,area,center,Lwidth,Rfraction,n-power,z-asym)
Generalized Error 2-width Area

GenError2_C(x,amplitude,center,Lwidth,Rfraction,n-power,z-asym)
Gen. Error 2-width cumulative

GenError2_CR(x,amplitude,center,Lwidth,Rfraction,n-power,z-asym)
Gen. Error 2-width reverse cumulative

This Asymmetric Error Model with 2-widths is part of the unique content in the product covered by its copyright.