How to use the POISSON.DIST function in Excel

In this article, we will learn How to use the POISSON.DIST function in Excel.

What is the POISSON distribution function ?

In Statistics, when predicting the number of events over a specific time we use the POISSON distribution function. For example an individual keeping track of the amount of mail they receive each day may notice that they receive an average number of 4 letters per day or as the number of cars arriving at a toll plaza in 1 minute. For problems like these we prefer to use the POISSON distribution function. The Poisson distribution can also be used for the number of events in other specified intervals such as distance, area or volume. Mathematically, we can calculate the probability for POISSON distribution function using the formula stated below.

Here 

e is Euler's number ( value of e = 2.71828...).

! is the factorial operator to calculate the factorial of the prefix value.
lambda is the POISSON distribution parameter.

This formulation seems complex to formulate in Excel. So Excel provides a built-in statistical POISSON.DIST function to work as a POISSON distribution calculator. 

POISSON.DIST Function in Excel

POISSON.DIST function built in statistical function returns the probability for the POISSON distribution. It takes the 2 arguments with the type of distribution function (cdf or pdf). Let's understand these arguments one by one listed below with the function syntax.

POISSON.DIST Function syntax:

x : number of events

exp_mean : expected average or mean value for the event

cumulative : logical value that determines the form of the function. If cumulative is TRUE, POISSON.DIST returns the cumulative distribution function; if FALSE, it returns the probability density function.

Example :

All of these might be confusing to understand. Let's understand how to use the function using an example. Here we have x number of events and expected mean. We need to calculate the cumulative for the POISSON distribution function.

Use the formula:

The f distribution probability comes out 0.101 or 10.1% for the exactly 5th event. 

You can find out the probability value for the POISSON distribution function for the value for at least 5 events following the same parameters with the formula shown below.

Use the formula:

The f distribution probability comes out 0.916 or 91.6% for at least 5 events. 

Here are all the observational notes using the POISSON.DIST function in Excel
Notes :

1. The function only works with numbers. If any argument other than cumulative is non numeric, the function returns #VALUE! error.
2. The function returns #NUM! Error.
   1. If argument x < 0
   2. If argument exp_mean < 0
3. Argument x event is truncated to integers if not.
4. The cumulative argument can be used with boolean numbers (0 and 1) or (FALSE or TRUE).
5. Value in decimal and value in percentage id the same value in Excel. Convert the value to percentage, if required.
6. You can feed the arguments to the function directly or using the cell reference as explained in the example.

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