Poisson Distribution
X ~ Poisson(λ)
Rare-Event / Count Family • Published July 18, 2026
The rare-event count distribution: history from Poisson's binomial limit through Bortkiewicz's horse-kick data, equidispersion (mean equals variance, and in fact every cumulant), the full property list, maximum-likelihood estimation of the rate, and exact simulation via Knuth's algorithm.
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About This Reference Sheet
The rare-event count distribution: history from Poisson's binomial limit through Bortkiewicz's horse-kick data, equidispersion (mean equals variance, and in fact every cumulant), the full property list, maximum-likelihood estimation of the rate, and exact simulation via Knuth's algorithm.
Support
x ∈ {0, 1, 2, ...}
Parameters
λ > 0 (mean rate)