hyperspy._components.skew_normal module¶

class hyperspy._components.skew_normal.SkewNormal(x0=0.0, A=1.0, scale=1.0, shape=0.0, module='scipy', **kwargs)¶

Bases: hyperspy._components.expression.Expression

Skew normal distribution component.

Asymmetric peak shape based on a normal distribution.
For definition see
https://en.wikipedia.org/wiki/Skew_normal_distribution
See also http://azzalini.stat.unipd.it/SN/

$f(x) &= 2 A \phi(x) \Phi(x) \\ \phi(x) &= \frac{1}{\sqrt{2\pi}}\mathrm{exp}{\left[ -\frac{t(x)^2}{2}\right]} \\ \Phi(x) &= \frac{1}{2}\left[1 + \mathrm{erf}\left(\frac{ \alpha~t(x)}{\sqrt{2}}\right)\right] \\ t(x) &= \frac{x-x_0}{\omega}$

Variable	Parameter
$x_0$	x0
$A$	A
$\omega$	scale
$\alpha$	shape

Parameters

x0 (float) – Location of the peak position (not maximum, which is given by the mode property).
A (float) – Height parameter of the peak.
scale (float) – Width (sigma) parameter.
shape (float) – Skewness (asymmetry) parameter. For shape=0, the normal distribution (Gaussian) is obtained. The distribution is right skewed (longer tail to the right) if shape>0 and is left skewed if shape<0.

The properties mean (position), variance, skewness and mode (=position of maximum) are defined for convenience.

property mean¶

property mode¶

property skewness¶

property variance¶