Poisson binomial distribution

In <a href="/facts/Probability_theory/mFBn51rE">probability theory</a> and <a href="/facts/Statistics/DNPsKGYU">statistics</a>, the Poisson binomial distribution is the <a href="/facts/Discrete_probability_distribution/EpsKKVRu">discrete probability distribution</a> of a sum of <a href="/facts/Statistical_independence/NUzQtnUL">independent</a> <a href="/facts/Bernoulli_trial/7fm8snCf">Bernoulli trials</a> that are not necessarily identically distributed. The concept is named after <a href="/facts/Sim%25C3%25A9on_Denis_Poisson/zmsDITrY">Siméon Denis Poisson</a>.
In other words, it is the <a href="/facts/Discrete_probability_distribution/EpsKKVRu">probability distribution</a> of the
number of successes in a collection of n <a href="/facts/Statistical_independence/NUzQtnUL">independent</a> yes/no experiments with success <a href="/facts/Probability/fgYvMhwb">probabilities</a> 
 
 
 
 
 p
 
 1
 
 
 ,
 
 p
 
 2
 
 
 ,
 …
 ,
 
 p
 
 n
 
 
 
 
 {\displaystyle p_{1},p_{2},\dots ,p_{n}}
 
. The ordinary <a href="/facts/Binomial_distribution/UMoFMjDj">binomial distribution</a> is a special case of the Poisson binomial distribution, when all success probabilities are the same, that is 
 
 
 
 
 p
 
 1
 
 
 =
 
 p
 
 2
 
 
 =
 ⋯
 =
 
 p
 
 n
 
 
 
 
 {\displaystyle p_{1}=p_{2}=\cdots =p_{n}}
 
.

Poisson binomial distribution open-in-new

Poisson binomial distribution