Formulas and functions > Functions from A to Z > POISSON (Poisson distribution)

Note: POISSON is supplemented by the new identical function POISSON.DIST, which is available in newer versions of Microsoft Excel (2010 or later).

Syntax:

POISSON(x, Lambda, Cumulative)

Description:

Returns the Poisson distribution.

The Poisson distribution describes the occurrence of independent, similar events of the same type in a given period (for example, the arrival of customers at a counter or the receipt of telephone calls).

It is particularly suitable for probability distributions where there are a large number of results from a sample and the probability that the evaluated event will occur is very small. Here the Poisson distribution can simulate the binomial distribution (with Lambda = n*p). In contrast to the binomial distribution, however, Poisson requires only one parameter (apart from x): the expected value Lambda (see example).

x is the value to be evaluated. Must be ≥ 0. Furthermore x should be an integer. Digits to the right of the decimal point are ignored.

Lambda (λ) is the expected value (mean value) for x. Lambda must be ≥ 0.

The logical value Cumulative lets you specify which type of function will be returned:

FALSE: The probability density function is returned.

TRUE: The cumulative distribution function is returned.

Example:

In a multi-story building, an average of 4 light bulbs become defective per week.

To determine the probability that just 3 light bulbs become defective in one week:

If you want to calculate this with the binomial distribution (function BINOM.DIST/BINOMDIST), you would have to write:

BINOMDIST(3, 100000, 4/100000, FALSE) returns 0.195368768

If, on the other hand, you use the Poisson distribution, you can do this without the parameters n and p and simply write:

POISSON(3, 4, FALSE) returns 0,195366815

As expected, the two results are very similar (as described above).

Another example: What is the probability of a maximum of 3 damages?

Here, instead of the density function, you use the distribution function (specify the Cumulative argument with TRUE):

POISSON(3, 4, TRUE) equals 0.43347