# POISSON

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## Content



This function returns the Poisson distribution.

## Syntax

POISSON(*nevents*,*mean*,*cumulative*)

## Remarks

This function has these arguments:

| **Argument** | **Description** |
| -------- | ----------- |
| *nevents* | Number of events Provide an integer, or the value is truncated. The number must be greater than zero. |
| *mean* | Expected numeric value The number must be greater than zero. |
| *cumulative* | Set to TRUE to return the cumulative Poisson probability that the number of random events occurring is between zero and *nevents* inclusive. Set to FALSE to return the Poisson probability mass function that the number of events occurring is exactly *nevents*. |

## Remarks

The cumulative Poisson probability is calculated as follows:
![Cumulative Poisson Probability Equation](https://cdn.mescius.io/document-site-files/images/0ed25d3e-6b2a-4cf0-8f1b-7ed5ab18cf12/artwork/func-poisson-true.png)
The Poisson probability mass function is calculated as follows:
![Poisson probability mass function](https://cdn.mescius.io/document-site-files/images/0ed25d3e-6b2a-4cf0-8f1b-7ed5ab18cf12/artwork/func-poisson-false.png)
where x is the number of events (*nevents* argument), mu is the mean (*mean* argument).

## Data Types

Accepts numeric data for all arguments. Returns numeric data.

## Examples

`POISSON(A3,B4,TRUE)`
`POISSON(R1C2,3,FALSE)`
`POISSON(7,4,TRUE)` gives the result 0.948866384
`POISSON(7,4,FALSE)` gives the result 0.059540363

## Version Available

This function is available in product version 1.0 or later.

## See Also

[BINOMDIST](/spreadnet/docs/latest/online-formula/formulas-functionsall/formulas-functsAtoC/FunctionBINOMDIST) \| [GAMMADIST](/spreadnet/docs/latest/online-formula/formulas-functionsall/formulas-functsDtoG/FunctionGAMMADIST) \| [HYPGEOMDIST](/spreadnet/docs/latest/online-formula/formulas-functionsall/formulas-functsFtoK/FunctionHYPGEOMDIST) \| [Statistical Functions](/spreadnet/docs/latest/online-formula/formulas-overview/formulas-functs/formulas-functtypes/formulas-functsstats)