# POISSON.DISTDAX Function (Statistical)

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> )
Parameter Attributes Description
X

The number of events.

Mean

The expected numeric value.

Cumulative

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 values

Scalar A single decimal 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.

## Examples

```--  POISSON.DIST returns the Poisson distribution
--  Use case: predicting the number of events over
--  a specific time, such as the number of customers
--  entering a store in 1 hour
--      POISSON.DIST ( Value, Mean, Cumulative )
DEFINE
VAR Mean            = 10 -- Expected number of customers in 1 hour
VAR Vals            = GENERATESERIES ( 0, 20, 1 )
VAR CumulativeTrue  = TRUE   -- Cumulative distribution function
VAR CumulativeFalse = FALSE  -- Probability density function
EVALUATE
ADDCOLUMNS (
Vals,
"Poisson Distr.",             -- Probability density function
FORMAT (
POISSON.DIST ( [Value], Mean, CumulativeFalse ),
"#,0.00000"
),
"Poisson Distr. Cumulative",  -- Cumulative distribution function
FORMAT (
POISSON.DIST ( [Value], Mean, CumulativeTrue ),
"#,0.00000"
)
)
```
Value Poisson Distr. Poisson Distr. Cumulative
0 0.00005 0.00005
1 0.00045 0.00050
2 0.00227 0.00277
3 0.00757 0.01034
4 0.01892 0.02925
5 0.03783 0.06709
6 0.06306 0.13014
7 0.09008 0.22022
8 0.11260 0.33282
9 0.12511 0.45793
10 0.12511 0.58304
11 0.11374 0.69678
12 0.09478 0.79156
13 0.07291 0.86446
14 0.05208 0.91654
15 0.03472 0.95126
16 0.02170 0.97296
17 0.01276 0.98572
18 0.00709 0.99281
19 0.00373 0.99655
20 0.00187 0.99841

Last update: Jul 12, 2024     » Show contributors

Contributors: Alberto Ferrari, Marco Russo

Microsoft documentation: https://docs.microsoft.com/en-us/dax/poisson-dist-function-dax

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# Context Transition

This function performs a Context Transition if called in a Row Context. Click to read more.

# Row Context

This expression is executed in a Row Context. Click to read more.

# Not recommended

The use of this function is not recommended. See Remarks and Related functions for alternatives.

# Not recommended

The use of this parameter is not recommended.

# Deprecated

This function is deprecated. Jump to the Alternatives section to see the function to use.

# Volatile

A volatile function may return a different result every time you call it, even if you provide the same arguments. Click to read more.

# Deprecated

This parameter is deprecated and its use is not recommended.

# DirectQuery compatibility

Limitations are placed on DAX expressions allowed in measures and calculated columns.
The state below shows the DirectQuery compatibility of the DAX function.

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