How do you know when to use a Poisson distribution

Victor Wall 2022-01-16 Answered
How do you know when to use a Poisson distribution or binomial distribution?
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aquariump9
Answered 2022-01-16 Author has 40 answers
As a short guide
If a mean or average probability of an event happening per unit time etc., is given, and you are asked to calculate a probability of n events happening in a given time etc then the Poisson Distribution is used.
If, on the other hand, an exact probability of an event happening is given and you are asked to calculate the probability of this event happening k times out of n, then the Binomial Distribution must be used.
The Poisson distribution can be derived as a limit of the binomial distribution.
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Buck Henry
Answered 2022-01-17 Author has 33 answers
The Poisson is used as an approximation of the Binomial if n is large and p is small. As with many ideas in statistics, “large” and “small” are up to interpretation. A rule of thumb is the Poisson distribution is a decent approximation of the Binomial if n > 20 and np < 10.
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