The Poisson distribution
[this page | pdf | back links]
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.
NAVIGATION LINKS
Contents | Prev | Next