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Reference.org
Borel distribution
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<p>The Borel distribution is a <a href="/facts/Discrete_probability_distribution/EpsKKVRu">discrete probability distribution</a>, arising in contexts including <a href="/facts/Branching_process/JzdGdWrQ">branching processes</a> and <a href="/facts/Queueing_theory/8NDl56EM">queueing theory</a>. It is named after the French mathematician <a href="/facts/%25C3%2589mile_Borel/lF9PBa1T">Émile Borel</a>. </p><p>If the number of offspring that an organism has is <a href="/facts/Poisson_distribution/CvCzXkHr">Poisson-distributed</a>, and if the average number of offspring of each organism is no bigger than 1, then the descendants of each individual will ultimately become extinct. The number of descendants that an individual ultimately has in that situation is a random variable distributed according to a Borel distribution. </p>