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:
For cumulative = TRUE:
Example
The example may be easier to understand if you copy it to a blank spreadsheet.
How?- Create a blank spreadsheet.
- Select the example in the Help topic.
Selecting an example from Help
- Press CTRL+C.
- In the spreadsheet, select cell A1, and press CTRL+V.
- To switch between viewing the formula that returns the result and the result in the cell, select the cell and press F2 and then ENTER, or click Commands and Options on the spreadsheet toolbar, click the Formula tab, and look in the Formula in active cell (active cell) box.
| 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) |