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
|
![](I/PoissonDistribution_files/image001.png)
|
Parameters
|
=
event rate ( )
|
Support
|
![](I/PoissonDistribution_files/image004.png)
|
Probability mass
function
|
![](I/PoissonDistribution_files/image005.png)
|
Cumulative distribution
function
|
![](I/PoissonDistribution_files/image006.png)
(can also be expressed using the incomplete gamma
function)
|
Mean
|
![](I/PoissonDistribution_files/image002.png)
|
Variance
|
![](I/PoissonDistribution_files/image002.png)
|
Skewness
|
![](I/PoissonDistribution_files/image007.png)
|
(Excess) kurtosis
|
![](I/PoissonDistribution_files/image008.png)
|
Characteristic function
|
![](I/PoissonDistribution_files/image009.png)
|
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.
NAVIGATION LINKS
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