SkewNormal Distribution

class SkewNormalDistribution(amplitude: float = 1.0, shape: float = 1.0, location: float = 0.0, scale: float = 1.0, normalize: bool = False)

Bases: BaseDistribution

Class for SkewNormal distribution.

Parameters:

• amplitude (float, optional) – The amplitude of the PDF. Defaults to 1.0. Ignored if normalize is True.

• shape (float, optional) – The mean parameter, \(\mu\). Defaults to 0.0.

• scale (float, optional) – The scale parameter, for scaling. Defaults to 1.0,

• location (float, optional) – The location parameter, for shifting. Defaults to 0.0.

• normalize (bool, optional) – If True, the distribution is normalized so that the total area under the PDF equals 1. Defaults to False.

Raises:

• NegativeAmplitudeError – If the provided value of amplitude is negative.

• NegativeStandardDeviationError – If the provided value of standard deviation is negative.

Attributes:

mean

The mean of the distribution.

median

The median of the distribution.

mode

The mode of the distribution.

stddev

The standard deviation of the distribution.

variance

The variance of the distribution.

Methods

cdf(x)	Compute the cumulative density function (CDF) for the distribution.
logcdf(x)	Compute the log cumulative density function (logCDF) for the distribution.
logpdf(x)	Compute the log probability density function (logPDF) for the distribution.
pdf(x)	Compute the probability density function (PDF) for the distribution.
scipy_like(a[, loc, scale])	Instantiate SkewNormalDistribution with scipy parametrization.
stats()	Computes and returns the statistical properties of the distribution, including,

Examples

Importing libraries:

import matplotlib.pyplot as plt
import numpy as np
from scipy.stats import skewnorm

from pymultifit.distributions import SkewNormalDistribution

Generating a standard Skew Normal(\(\xi=1, \mu = 0, \sigma = 1\)) distribution with pyMultiFit and scipy:

x_values = np.linspace(start=-10, stop=10, num=500)

y_multifit = SkewNormalDistribution(normalize=True)
y_scipy = skewnorm

Plotting PDF and CDF:

f, ax = plt.subplots(1, 2, figsize=(12, 5))

ax[0].plot(x_values, y_scipy.pdf(x=x_values, a=1), label='Scipy Skew Normal')
ax[0].plot(x_values, y_multifit.pdf(x_values), 'k:', label='pyMultiFit Skew Normal')
ax[0].set_ylabel('f(x)')

ax[1].plot(x_values, y_scipy.cdf(x=x_values, a=1), label='Scipy Skew Normal')
ax[1].plot(x_values, y_multifit.cdf(x_values), 'k:', label='pyMultiFit Skew Normal')
ax[1].set_ylabel('F(x)')

f.suptitle('Skew Normal(1, 0, 1)')

for i in ax:
    i.set_xlabel('X')
    i.legend()
plt.tight_layout()

Generating a translated Skew Normal(\(\xi=3, \mu=-3, \sigma=3\)) distribution:

y_multifit = SkewNormalDistribution(shape=3, scale=3, location=-3, normalize=True)

Plotting PDF and CDF:

f, ax = plt.subplots(1, 2, figsize=(12, 5))

ax[0].plot(x_values, y_scipy.pdf(x=x_values, a=3, loc=-3, scale=3), label='Scipy translated Skew Normal')
ax[0].plot(x_values, y_multifit.pdf(x_values), 'k:', label='pyMultiFit translated Skew Normal')
ax[0].set_ylabel('f(x)')

ax[1].plot(x_values, y_scipy.cdf(x=x_values, a=3, loc=-3, scale=3), label='Scipy translated Skew Normal')
ax[1].plot(x_values, y_multifit.cdf(x_values), 'k:', label='pyMultiFit translated Skew Normal')
ax[1].set_ylabel('F(x)')

f.suptitle(r'Skew Normal(3, -3, 3)')

for i in ax:
    i.set_xlabel('X')
    i.legend()
plt.tight_layout()

cdf(x)

Compute the cumulative density function (CDF) for the distribution.

Parameters:

x – Input array at which to evaluate the CDF.

logcdf(x: float | ndarray) → float | ndarray

Compute the log cumulative density function (logCDF) for the distribution.

Parameters:

x – Input array at which to evaluate the logCDF.

logpdf(x: float | ndarray) → float | ndarray

Compute the log probability density function (logPDF) for the distribution.

Parameters:

x – Input array at which to evaluate the logPDF.

pdf(x)

Compute the probability density function (PDF) for the distribution.

Parameters:

x – Input array at which to evaluate the PDF.

classmethod scipy_like(a: float, loc: float = 0.0, scale: float = 1.0)

Instantiate SkewNormalDistribution with scipy parametrization.

Parameters:

afloat

The skewness parameter.

locfloat, optional

The location parameter. Defaults to 0.0.

scalefloat, optional

The scale parameter. Defaults to 1.0.

Returns:

SkewNormalDistribution

An instance of normalized SkewNormalDistribution.

stats()

Computes and returns the statistical properties of the distribution, including,

1. mean,

2. median,

3. variance, and

4. standard deviation.

Returns:

A dictionary containing statistical properties such as mean, variance, etc.

Return type:

Dict[str, float]

Notes

If any of the parameter is not computable for a distribution, this method returns None.

property mean

The mean of the distribution.

property median

The median of the distribution.

property mode

The mode of the distribution.

property stddev

The standard deviation of the distribution.

property variance

The variance of the distribution.

This class internally utilizes the following functions from utilities_d module:

• skew_normal_pdf_

• skew_normal_cdf_

Recommended Import

from pymultifit.distributions import SkewNormalDistribution

Full Import

from pymultifit.distributions.skewNormal_d import SkewNormalDistribution