The POISSON.DIST function returns the Poisson distribution. A common application of the Poisson distribution is predicting the number of events over a specific time, such as the number of cars arriving at a toll plaza in 1 minute.

• This function was introduced in Excel 2010 and so is not available in earlier versions.
• The POISSON.DIST function replaces the POISSON function included in earlier versions of Excel.

### Syntax

=POISSON.DIST(x,mean,cumulative)

#### Arguments

Argument Description
x The number of events – must be ≥ 0
mean The expected number of events – must be ≥ 0
cumulative A logical value that determines the form of the probability distribution returned

 TRUE – Returns the cumulative poisson probability that the number of random events occurring will be between zero and x inclusive FALSE – Returns the poisson probability mass function that the number of events occurring will be exactly x

#### Examples

A B C D
1 Data Description
2 3
3 10
4
5 Formula Result Notes
6 =POISSON.DIST(A2,A3,TRUE) 0.010336 Cumulative Poisson probability with the arguments specified in A2 and A3
7 =POISSON.DIST(A2,A3,FALSE) 0.007567 Poisson probability mass function with the arguments specified in A2 and A3

#### Common Function Error(s)

Problem What went wrong
#VALUE! Occurs if either of the supplied x or mean arguments are non-numeric
#NUM! Occurs if either of the supplied x or mean arguments are < 0

The Poisson distribution is a discrete probability function that can be used to find the probability of a number of events occurring in a specified time period.

The probability mass function shows the probability of exactly x occurrences, and is calculated as:

where is the expected number of occurrences within the specified time period.

The cumulative distribution functions shows the probability of at most x occurrences, and is calculated as: