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scipy.stats.

# Mixture

class scipy.stats.Mixture(components, *, weights=None)

  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:
    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`() | 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:

      >>> 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}')
      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()