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The Poisson distribution

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The Poisson distribution expresses the probability of a given number of events occurring in a fixed interval of time if the events occur with a known average rate and independently of the time since the last event.

 

Distribution name

Poisson distribution

Common notation

Parameters

 = event rate ()

Support

Probability mass function

Cumulative distribution function

(can also be expressed using the incomplete gamma function)

Mean

Variance

Skewness

(Excess) kurtosis

Characteristic function

Other comments

The median is approximately .

 

The mode is  if  is not integral. Otherwise the distribution is bi-modal with modes  and .

 

Nematrian web functions

 

Functions relating to the above distribution may be accessed via the Nematrian web function library by using a DistributionName of “poisson”. For details of other supported probability distributions see here.

 


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