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.
The POISSON.DIST function syntax has the following arguments:
- X (required argument) – This is the number of events for which we want to calculate the probability. The value must be greater than or equal to 0.
- Mean (required argument) – This is the expected number of events. The argument must be greater than or equal to zero.
- Cumulative (required argument) – This is the logical argument that specifies the type of distribution to be calculated. It can either be:
- TRUE – Returns the cumulative Poisson probability that the number of random events occurring will be between zero and x inclusive.
- FALSE – Returns the Poisson probability mass function that the number of events occurring will be exactly x.
Example: Let’s look at some Excel POISSON.DIST function examples and explore how to use the POISSON.DIST function as a worksheet function in Microsoft Excel:
Suppose we are given the following data:
- Number of events: 20
- Expected mean: 25
To find out the Cumulative Poisson probability, we will use the following formula:
To find out the Poisson probability mass function, we will use the following formula:
- If x is not an integer, it is truncated.
- 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:
For cumulative = TRUE: