A mixture with numeric weights:

Cumulative distribution function:

A mixture with symbolic weights:

Probability density function:

The weights control the contribution by each distribution:

Two univariate continuous distributions:

The mixture combines the densities according to their weights:

Two bivariate continuous distributions:

The mixture combines the densities according to their weights:

Two univariate discrete distributions:

Probability density function:

Plot a density function for different weights:

Mean and variance:

Two multivariate discrete distributions:

Probability density function:

Generate random numbers:

Several univariate continuous distributions:

Moments:

Factorial moments:

Central moments:

Cumulants:

Several univariate discrete distributions:

Generating functions:

Estimate weights in a mixture:

Define a mixture of two different continuous distributions:

Probability density function:

Hazard function:

In the limit the exponential distribution component dominates:

Define a mixture of two distributions with different supports:

Probability density function for a few values of the weight:

Define a mixture of two different univariate discrete distributions:

Probability density function:

Cumulative distribution function:

Moments can be obtained numerically:

Define a mixture of two different multivariate discrete distributions:

Probability density function:

Covariance:

Define a mixture distribution of multivariate uniform distributions:

Cumulative distribution function:

The mixture combines the densities according to their weights:

Define a mixture with

EmpiricalDistribution:

The mixture combines the cumulative distribution functions according to their weights:

Plot the cumulative distribution function:

Define a mixture with

HistogramDistribution:

The mixture combines the densities according to their weights:

Define a mixture distribution with components given by

MixtureDistribution:

The PDF is piecewise continuous:

The mean is a convex combination of the means of the components:

Find which components cause the mean of the mixture to be indeterminate:

Find a mixture distribution of the

OrderDistribution of the minimum and the maximum:

Compare the probability density functions:

The mean of the mixture distribution:

Compare to the average of the means of order distributions:

Find the mixture distribution of a

TruncatedDistribution:

The probability density function is not continuous:

The mean can be computed explicitly:

Find the probability density function of the mixture distribution with a

ProductDistribution:

Define a mixture distribution with a

TransformedDistribution:

Probability density function:

Define a mixture distribution of a

MarginalDistribution:

Characteristic function:

Define a mixture with a

CensoredDistribution:

Probability density function:

PDFs of scaled mixture components and mixture distribution:

Define a mixture distribution with a

CopulaDistribution:

One component mixture simplifies to the input distribution:

A mixture with zero weights will reduce the number of input distributions:

A mixture with one zero weight will return an empty mixture: