# Poisson distribution

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Related to Poisson random variable: Exponential random variable, Hypergeometric random variable

## Pois·son dis·tri·bu·tion

(pwah-son[h]'),**1.**a discontinuous distribution important in statistical work and defined by the equation

*p*(

*x*) =

*e*

^{-μ}μ

^{x}/

*x*!, where

*e*is the base of natural logarithms,

*x*is the sequence of integers, μ is the mean, and

*x*! represents the factorial of

*x*.

**2.**a distribution function used to describe the occurrence of rare events, or the sampling distribution of isolated counts in a continuum of time or space.

## Poisson distribution

A sampling distribution based on the number of occurrences, r, of an event during a period of time, which depends on only one parameter, the mean number of occurrences in periods of the same length.## Poisson distribution

Statistics The distribution that arises when parasites are distributed randomly among hosts. See Distribution.## Poisson distribution

(statistics) the frequency of sample classes containing a particular number of events (0,1,2,3 … n), where the average frequency of the event is small in relation to the total number of times that the event could occur. Thus, if a pool contained 100 small fish then each time a net is dipped into the pool up to 100 fish could be caught and returned to the pool. In reality, however, only none, one or two fish are likely to be caught each time. The Poisson distribution predicts the probability of catching 0,1,2,3 … 100 fish each time, producing a FREQUENCY DISTRIBUTION graph that is skewed heavily towards the low number of events.## Poisson,

Siméon Denis, French mathematician, 1781-1840.**Poisson distribution**- a discontinuous distribution important in statistical work.

**Poisson ratio**

**Poisson-Pearson formula**- to determines the statistical error in calculating the endemic index of malaria.

## Poisson distribution

a statistical distribution which often describes the sampling frequency of individual, isolated counts in time and space.

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