# DAX Statistical - POISSON.DIST function

## Description

Returns the Poisson distribution. A common application of the Poisson distribution is predicting the number of events over a specific time.

## Syntax

POISSON.DIST (<x>, <mean>, <cumulative>)


## Parameters

Sr.No. Parameter & Description
1

x

The number of events.

2

mean

The expected numeric value.

3

cumulative

A logical value that determines the form of the probability distribution returned.

TRUE: POISSON.DIST returns the cumulative Poisson probability that the number of random events occurring will be between zero and x inclusive.

FALSE: POISSON.DIST returns the Poisson probability mass function that the number of events occurring will be exactly x.

## Return Value

Returns the Poisson distribution.

## Remarks

• If x is not an integer, it is truncated.

• If x or mean is non-numeric, POISSON.DIST returns the #VALUE! error value.

• If x < 0, POISSON.DIST returns the #NUM! error value.

• If mean < 0, POISSON.DIST returns the #NUM! error value.

• POISSON.DIST is calculated as follows.

• For cumulative = FALSE −

$$POISSON\:=\:\frac{e^{-\lambda} \lambda^{x}}{x!}$$

• For cumulative = TRUE −

$$CUMPOISSON\:=\:\sum_{k=0}^x\frac{e^{-\lambda} \lambda^{x}}{k!}$$

## Example

= POISSON.DIST (2,5, TRUE ()) returns 0.124652019483081.

dax_functions_statistical.htm

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