POISSON Function

Basic Description

The Excel POISSON function calculates the Poisson Probability Mass Function or the Cumulative Poisson Probability Function for a supplied set of parameters.

Syntax: POISSON( x, mean, cumulative )

Where the function arguments are listed in the table below :

x The number of events that we want the probability for (must be ≥ 0)

This value should be an integer; If a decimal is supplied, it will be truncated to an integer by Excel

mean The expected number of events (must be ≥ 0)
cumulative A logical argument that specifies the type of distribution to be calculated. This can be either:

TRUE use the cumulative distribution function
FALSE use the probability mass function

 

Poisson Function Examples

Example 1 – Poisson Probability Mass Function

The chart on the right shows the the Poisson Probability Mass Function with an expected value (mean) of 25.

If you want to use Excel to calculate the value of this function at x = 40, this can be done using the Excel Poisson function, as follows:

=POISSON( 20, 25, FALSE )

This gives the result 0.051917469.

Plot of Poisson Probability Mass Function with Lambda=25Poisson Probability Mass Function with mean (λ) = 25
Example 2 – Cumulative Poisson Probability Function

The chart on the right shows the the Cumulative Poisson Probability Function with an expected value (mean) of 40.

If you want to use Excel to calculate the value of this function at x = 25, this can be done using the Excel Poisson function, as follows:

=POISSON( 35, 40, TRUE )

This gives the result 0.242414198.

Plot of Cumulative Poisson Probability Function with Lambda=40Cumulative Poisson Probability Function with mean (λ) = 40

 

 

Poisson Function Errors

If you get an error from the Excel Poisson function this is likely to be one of the following :

#NUM! Occurs if either the supplied x argument or the supplied mean argument is < 0
#VALUE! Occurs when either of the supplied x or mean arguments are non-numeric

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