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

Syntax:

POISSON.DIST(x, Lambda, Cumulative)

Description:

This returns the probabilities of a Poisson distributed random variable.

The Poisson distribution describes the occurrence of independent, similar events within a given period (for example, the arrival of customers at a counter or the occurrence of incoming phone calls).

It is particularly suitable for probability distributions where there are a large number of results from a sample, and there is a low probability that the event in question will occur. 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 whose probability is to be calculated. x must be ≥ 0. Furthermore, x should be an integer. If this is not the case, PlanMaker automatically truncates the decimal places.

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

You use the logical value Cumulative to 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 wanted to calculate this with the binomial distribution (function BINOM.DIST/BINOMDIST), you would have to write the following:

BINOM.DIST(3, 100000, 4/100000, FALSE) returns 0.195368768

If you use the Poisson distribution, however, you can do so without the parameters n and p and simply write the following:

POISSON.DIST(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 light bulbs becoming defective?

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

POISSON.DIST(3, 4, TRUE) returns 0.43347

Compatibility notes:

Microsoft Excel supports this function only in version 2010 or later. The function is unknown in older versions.