# POISSON.DIST

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.

## Syntax

```
POISSON.DIST(x,mean,cumulative)
```

### Parameters

Term | Definition |
---|---|

x | Required. The number of events. |

mean | Required. The expected numeric value. |

cumulative | Required. A logical value that determines the form of the probability distribution returned. If cumulative is TRUE, POISSON.DIST returns the cumulative Poisson probability that the number of random events occurring will be between zero and x inclusive; if FALSE, it 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 rounded.

If x or mean is nonnumeric, 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:

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

For cumulative = TRUE:

$$\text{CUMPOISSON} = \sum^{x}_{k=0} \frac{e^{-\lambda} \lambda^{x}}{k!}$$

This function is not supported for use in DirectQuery mode when used in calculated columns or row-level security (RLS) rules.