Model the probability of rare events in a fixed interval.
Distribution Parameters
Probability Analysis
Exactly k events P(X=k) (k=2)22.4042%Common Occurrence
P(X≤k) Cumulative42.3%
P(X≥k) At Least80.1%
Mean (μ)3
Variance (σ²)3
Std Dev (σ)1.73
Poisson Probability Distribution
About this calculator
Overview
The Poisson distribution models the number of times an independent event occurs in a fixed interval of time or space. It is often called the 'distribution of rare events' and is used in physics, finance, and queueing theory.
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Pro Tips
Events must occur independently of each other.
The average rate (λ) must be constant over the interval.
If the mean and variance of your data differ significantly, it's called 'overdispersion'.
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Fun Facts
"In 1898, Ladislaus Bortkiewicz used Poisson to analyze the number of soldiers killed by horse kicks in the Prussian Army."
"The Poisson distribution is the limit of the binomial distribution when the number of trials (n) is large and the probability (p) is small."
"In a true Poisson process, the mean and the variance are always exactly equal."
