`scipy.stats._distribution_infrastructure:Mixture`

source: /scipy/stats/_distribution_infrastructure.py :5093

Signature

def Mixture ( components , * , weights = None )

Members

Summary

Representation of a mixture distribution.

Extended Summary

A mixture distribution is the distribution of a random variable defined in the following way: first, a random variable is selected from components according to the probabilities given by weights, then the selected random variable is realized.

Parameters

components : sequence of `ContinuousDistribution`: The underlying instances of ContinuousDistribution. All must have scalar shape parameters (if any); e.g., the pdf evaluated at a scalar argument must return a scalar.
weights : sequence of floats, optional: The corresponding probabilities of selecting each random variable. Must be non-negative and sum to one. The default behavior is to weight all components equally.

Attributes

components : sequence of `ContinuousDistribution`: The underlying instances of ContinuousDistribution.
weights : ndarray: The corresponding probabilities of selecting each random variable.

Methods

support
sample
moment
mean
median
mode
variance
standard_deviation
skewness
kurtosis
pdf
logpdf
cdf
icdf
ccdf
iccdf
logcdf
ilogcdf
logccdf
ilogccdf
entropy

Notes

The following abbreviations are used throughout the documentation.

PDF: probability density function
CDF: cumulative distribution function
CCDF: complementary CDF
entropy: differential entropy
log-F: logarithm of F (e.g. log-CDF)
inverse F: inverse function of F (e.g. inverse CDF)

Examples

A mixture of normal distributions:

import numpy as np
from scipy import stats
import matplotlib.pyplot as plt
X1 = stats.Normal(mu=-2, sigma=1)
X2 = stats.Normal(mu=2, sigma=1)
mixture = stats.Mixture([X1, X2], weights=[0.4, 0.6])
print(f'mean: {mixture.mean():.2f}, '
      f'median: {mixture.median():.2f}, '
      f'mode: {mixture.mode():.2f}')
x = np.linspace(-10, 10, 300)

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plt.plot(x, mixture.pdf(x))
plt.title('PDF of normal distribution mixture')

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plt.show()

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