Find the parameter mixture of ExponentialDistribution with uniformly distributed weight:

Probability density function:

The weight domain must satisfy the parameter assumptions of the main distribution:

Pick a weight distribution supported on the positive reals:

The resulting parameter mixture CDF:

Use a discrete weight for a discrete parameter:

Compare the probability density functions:

Compare probabilities of obtaining a value less than 4 from each distribution:

Vary only one parameter:

Cumulative distribution function:

Mean and variance:

Use a multivariate distribution as a weight to vary more than one parameter:

Use more than one weight distribution to vary multiple parameters:

Visualize the probability density function:

Estimate parameters in a parameter mixture distribution:

Create a random sample for a choice of weight distribution parameters:

Find the distribution parameters:

Compare the histogram of the sample with the PDF of the estimated distribution:

Define a parameter mixture with a continuous univariate weight distribution:

Define a parameter mixture with a discrete univariate weight distribution:

Find the probability density function:

Moment has closed form for a symbolic order:

Define a parameter mixture with a discrete univariate weight distribution:

Probability density function:

Define a parameter mixture with a multivariate weight distribution:

Probability density function:

Verify that the integral of the PDF is 1:

Use more than one weight distribution:

Mean:

Variance:

Define a parameter mixture of a continuous univariate distribution:

Cumulative distribution function:

Find a mixture of a continuous univariate distribution:

Probability density function:

Define a parameter mixture of a discrete univariate distribution:

Generate a random sample:

Find the mean and variance:

Find a parameter mixture of a discrete univariate distribution:

Probability density function:

Mean and variance:

For a fixed value of , Moment has closed form for symbolic order:

Define a parameter mixture of a bivariate continuous distribution:

Use a random sample and a smooth histogram to visualize the density function:

Define a parameter mixture of a bivariate distribution:

Probability density function:

Mean:

Covariance matrix:

Find a parameter mixture distribution of a multivariate discrete distribution:

Generate a random sample:

Histograms for each component:

LaplaceDistribution can be represented as a parametric mixture:

Use an EmpiricalDistribution as a weight:

Probability density function:

Use a HistogramDistribution as a weight:

Probability density function:

Define a parameter mixture with a SmoothKernelDistribution as a weight:

Plot the probability density function:

Plot the cumulative distribution function:

Use a ProductDistribution as a weight distribution in a parameter mixture:

Use the histogram of a random sample from  to visualize the PDF:

Find a parameter mixture distribution of a TransformedDistribution:

Visualize the density function using a random sample:

Find a parameter mixture using a TransformedDistribution as a weight distribution:

Probability density function:

Use a MixtureDistribution as a weight distribution in a parameter mixture:

Probability density function:

Mean and variance:

Vary weights in a MixtureDistribution according to a probability distribution:

Probability density function:

Compare to the MixtureDistribution with fixed weights at the average values:

Both density functions are equal:

Define a parameter mixture of a TruncatedDistribution:

Mean and variance:

Define a parameter distribution of a TruncatedDistribution:

Visualize the probability density function using random sample:

Use a TruncatedDistribution as a weight distribution in a parameter mixture:

Probability density function:

Mean:

Find a parameter mixture distribution of an OrderDistribution:

Probability density function:

Use an OrderDistribution as a weight distribution:

Probability density function:

Parameter mixture of QuantityDistribution evaluates to QuantityDistribution:

WaringYuleDistribution is a parameter mixture of geometric distribution and UniformDistribution:

Compare with the built-in answer: