POISSON function

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(x,mean,cumulative)

X     is the number of events.

Mean     is the expected numeric value.

Cumulative     is a logical value that determines the form of the probability distribution returned. If cumulative is TRUE, POISSON 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.

Remarks

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

  • If x or mean is nonnumeric, POISSON returns the #VALUE! error value.

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

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

  • POISSON is calculated as follows.

    For cumulative = FALSE:

    Equation

    For cumulative = TRUE:

    Equation

Example

The example may be easier to understand if you copy it to a blank worksheet.

How to copy an example

  1. Create a blank workbook or worksheet.

  2. Select the example in the Help topic.

    Note   Do not select the row or column headers.

    Selecting an example from Help

    Selecting an example from Help

  3. Press CTRL+C.

  4. In the worksheet, select cell A1, and press CTRL+V.

  5. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

1

2

3

A

B

Data

Description

2

Number of events

5

Expected mean

Formula

Description (Result)

=POISSON(A2,A3,TRUE)

Cumulative Poisson probability with the terms above (0.124652)

=POISSON(A2,A3,FALSE)

Poisson probability mass function with the terms above (0.084224)

Applies To: Excel 2007



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