scipy.stats.

Mixture#

classscipy.stats.Mixture(components, *, weights=None)[source] #

Representation of a mixture distribution.

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:
componentssequence 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.

weightssequence 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:
componentssequence of ContinuousDistribution

The underlying instances of ContinuousDistribution.

weightsndarray

The corresponding probabilities of selecting each random variable.

Methods

support()

Support of the random variable

sample([shape, rng, method])

Random sample from the distribution.

moment([order, kind, method])

Raw, central, or standard moment of positive integer order.

mean(*[, method])

Mean (raw first moment about the origin)

median(*[, method])

Median (50th percentile)

mode(*[, method])

Mode (most likely value)

variance(*[, method])

Variance (central second moment)

standard_deviation(*[, method])

Standard deviation (square root of the second central moment)

skewness(*[, method])

Skewness (standardized third moment)

kurtosis(*[, method])

Kurtosis (standardized fourth moment)

pdf(x, /, *[, method])

Probability density function

logpdf(x, /, *[, method])

Log of the probability density function

cdf(x[, y, method])

Cumulative distribution function

icdf(p, /, *[, method])

Inverse of the cumulative distribution function.

ccdf(x[, y, method])

Complementary cumulative distribution function

iccdf(p, /, *[, method])

Inverse complementary cumulative distribution function.

logcdf(x[, y, method])

Log of the cumulative distribution function

ilogcdf(p, /, *[, method])

Inverse of the logarithm of the cumulative distribution function.

logccdf(x[, y, method])

Log of the complementary cumulative distribution function

ilogccdf(p, /, *[, method])

Inverse of the log of the complementary cumulative distribution function.

entropy(*[, method])

Differential 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)

References

[1]

Mixture distribution, Wikipedia, https://en.wikipedia.org/wiki/Mixture_distribution

Examples

A mixture of normal distributions:

>>> importnumpyasnp
>>> fromscipyimport stats
>>> importmatplotlib.pyplotasplt
>>> 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}')
mean: 0.40, median: 1.04, mode: 2.00
>>> x = np.linspace(-10, 10, 300)
>>> plt.plot(x, mixture.pdf(x))
>>> plt.title('PDF of normal distribution mixture')
>>> plt.show()
../../_images/scipy-stats-Mixture-1.png
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