Mixed Poisson distribution

<p>A mixed Poisson distribution is a <a href="/facts/Univariate_distribution/YjaPqYfq">univariate</a> discrete <a href="/facts/Probability_distribution/EpsKKVRu">probability distribution</a> in stochastics. It results from assuming that the conditional distribution of a random variable, given the value of the rate parameter, is a <a href="/facts/Poisson_distribution/CvCzXkHr">Poisson distribution</a>, and that the <a href="/facts/Scale_parameter/6lxcyKUf">rate parameter</a> itself is considered as a random variable. Hence it is a special case of a <a href="/facts/Compound_probability_distribution/ccJIMBxT">compound probability distribution</a>. Mixed Poisson distributions can be found in <a href="/facts/Actuarial_science/KxmCE0ME">actuarial mathematics</a> as a general approach for the distribution of the number of claims and is also examined as an <a href="/facts/Mathematical_modelling_of_infectious_disease/cGrvYHsX">epidemiological model</a>. It should not be confused with <a href="/facts/Compound_Poisson_distribution/tLHJbhIP">compound Poisson distribution</a> or <a href="/facts/Compound_Poisson_process/DrfL22v3">compound Poisson process</a>.
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Mixed Poisson distribution open-in-new

Mixed Poisson distribution