Asymmetric Pearson VII¶
Description¶
The asymmetric Pearson VII function (sometimes it is also referred to as the split-Pearson VII function) is a function that combines two Pearson VII distributions so to fit sharp peak curves [1]. It is useful for analysis of X-ray diffraction peaks which consist of two separable components.
In one of the representations, the asymmetric Pearson VII function
where
The four free parameters that the Pearson VII function
- the height of the peak - the location (centre) of the peak - the full width at half maximum - the function’s shape parameter
The parameter
In other words, it is assumed that the asymmetric Pearson VII function uses two halves of the Pearson VII with a common peak hight, peak centre, and full width at half maximum. As a result, the asymmetric Pearson VII distribution takes five parameters:
Analytic Derivatives¶
Below is the list of analytic derivatives of
where
Asymptotic Behavior¶
The numerical calculation of
The figure below illustrates the comparison of shapes between various symmetric [3] and asymmetric Pearson VII distributions plotted for
![AsymmetricPearsonVII.png](../../_images/AsymmetricPearsonVII.png)
Properties (fitting parameters)¶
Name |
Default |
Description |
---|---|---|
PeakHeight |
1.0 |
Hight of the peak |
PeakCentre |
0.0 |
Location of the peak |
Width |
0.1 |
Full width at half maximum |
LeftShape |
1.0 |
Left shape parameter |
RightShape |
1.0 |
Right shape parameter |
References¶
Categories: FitFunctions | XrayDiffraction
Source¶
C++ header: AsymmetricPearsonVII.h
C++ source: AsymmetricPearsonVII.cpp