hyperspy._components.skew_normal module

class hyperspy._components.skew_normal.SkewNormal(x0=0.0, A=1.0, scale=1.0, shape=0.0, module=['numpy', '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.
**kwargs – Extra keyword arguments are passed to the Expression component.

Notes

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

estimate_parameters(signal, x1, x2, only_current=False)

Estimate the skew normal distribution by calculating the momenta.

Parameters

signal (Signal1D instance) –
x1 (float) – Defines the left limit of the spectral range to use for the estimation.
x2 (float) – Defines the right limit of the spectral range to use for the estimation.
only_current (bool) – If False estimates the parameters for the full dataset.

Return type

bool

Notes

Adapted from Lin, Lee and Yen, Statistica Sinica 17, 909-927 (2007) https://www.jstor.org/stable/24307705

Examples

>>> g = hs.model.components1D.SkewNormal()
>>> x = np.arange(-10, 10, 0.01)
>>> data = np.zeros((32, 32, 2000))
>>> data[:] = g.function(x).reshape((1, 1, 2000))
>>> s = hs.signals.Signal1D(data)
>>> s.axes_manager._axes[-1].offset = -10
>>> s.axes_manager._axes[-1].scale = 0.01
>>> g.estimate_parameters(s, -10, 10, False)

property mean: Mean (position) of the component.

property mode: Mode (position of maximum) of the component.

property skewness: Skewness of the component.

property variance: Variance of the component.