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Borel distribution : ウィキペディア英語版
Borel distribution

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| variance = \frac
| entropy =
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The Borel distribution is a discrete probability distribution, arising in contexts including branching processes and queueing theory.
If the number of offspring that an organism has is Poisson-distributed, 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.
==Definition==
A discrete random variable ''X'' is said to have a Borel distribution
with parameter ''μ'' ∈ () if the probability mass function of ''X'' is given by
:P_\mu(n)= \Pr(X=n)= \frac}
for ''n'' = 1, 2, 3 ....

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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