Compound probability distribution

In <a href="/facts/Probability/fgYvMhwb">probability</a> and <a href="/facts/Statistics/DNPsKGYU">statistics</a>, a compound probability distribution (also known as a <a href="/facts/Mixture_distribution/BMdA5kTI">mixture distribution</a> or contagious distribution) is the <a href="/facts/Probability_distribution/EpsKKVRu">probability distribution</a> that results from assuming that a <a href="/facts/Random_variable/TwTBXnLT">random variable</a> is distributed according to some parametrized distribution, with (some of) the parameters of that distribution themselves being random variables.
If the parameter is a <a href="/facts/Scale_parameter/6lxcyKUf">scale parameter</a>, the resulting mixture is also called a scale mixture.
The compound distribution ("unconditional distribution") is the result of <a href="/facts/Marginal_distribution/U9XBWAd1">marginalizing</a> (integrating) over the latent random variable(s) representing the parameter(s) of the parametrized distribution ("conditional distribution").

Compound probability distribution open-in-new

Compound probability distribution