Poisson distribution

The Poisson distribution is any member of a class of discrete probability distributions named after Simeon Denis Poisson.

It is well suited for modeling various physical phenomena.

A basic introduction to the concept

Example

A certain event happens at unpredictable intervals. But for some reason, no matter how recent or long ago last time was, the probability that it will occur again within the next hour is exactly 10%.

Then the number of events per day is Poisson distributed.

Formal definition

Let X be a stochastic variable taking non-negative integer values with probability density function

$P(X=k)=f(k)=e^{-\lambda }{\frac {\lambda ^{k}}{k!}}.$

Then X follows the Poisson distribution with parameter $\lambda$.

Characteristics of the Poisson distribution

If X is a Poisson distribution stochastic variable with parameter $\lambda$, then

• The expected value $E[X]=\lambda$
• The variance $Var[X]=\lambda$

See also

• Binomial distribution
• Exponential distribution
• Probability distribution
• Probability
• Probability theory

Related topics

• Continuous probability distributions

External links

• mathworld