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 bimodal 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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