Generating random numbers from the exponential distribution in Excel should not be such a difficult task, but the lack of a direct function does it make it difficult. In this post, you will see the steps to generate random numbers from the exponential distribution in Excel.

## Understanding Exponential Distribution

The probably density function (PDF) of exponential distribution is:`f(x; lambda) = lambda * exp(-lambda * x)`

where:

x is greater than or equal to zero

lambda is the rate parameter or 1/mean.

The cumulative distribution function (CDF) of exponential distribution is:

`F(x; lambda) = 1 - exp(-lambda * x)`

Percent Point Function (PPF) or Inverse of the cumulative distribution function, given by:

`G(x) = - 1/lambda * logn(1- x)`

We will use the PPF to generate exponential distribution random numbers.

## Step 1: Generate Random Numbers from Uniform Distribution

- The first step is to create a set of uniform random numbers between 0 and 1. To generate these random numbers, simple enter this following command in your Excel sheet cell A2:

`=RAND()`

- Copy the formula down to A21, so that we have 20 random numbers from A2:A21.

Step 2: Calculate Mean of the Random Numbers

In a blank cell, say A22, calculate the mean of the numbers. Enter this formula:

`=AVERAGE(A2:A21)`

## Step 2: Generate Random Numbers from Exponential Distribution

- In cell B2, enter this formula (there is a minus sign in front of A22):

`=-A22 * LN(1 - A2)`

where:

LN is the natural logarithm value.

- In the formula, make A22 absolute value by place the $ sign in front of the letter and numbers, such as $A$22.
- Drag the formula down to B21

See this following image for an example:

There you have it: you have successfully generated random numbers in Excel from the exponential distribution.

### Excel And Statistics Books You May Be Interested In:

- Herkenhoff, Linda (Author)
- English (Publication Language)
- 431 Pages - 11/26/2013 (Publication Date) - Springer (Publisher)

- Microsoft Press
- Winston, Wayne (Author)
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- 864 Pages - 12/09/2016 (Publication Date) - Microsoft Press (Publisher)

- Winston, Wayne (Author)
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- 880 Pages - 04/15/2019 (Publication Date) - Microsoft Press (Publisher)

- Shields, Greg (Author)
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- 80 Pages - 09/06/2018 (Publication Date) - CreateSpace Independent Publishing Platform (Publisher)

Last update on 2020-11-24 / Affiliate links / Images from Amazon Product Advertising API

Very clear explanation. If I wanted the exponential distribution to have a different mean to that of that generated by the Rand() I could use the normal distribution random number generator in Excel and select say a mean of 5 but I would be forced to insert a standard deviation which I would choose say a 4 (99.999% of the area under the curve). However the results would include negative numbers which are unacceptable in a skewed distribution, particularly when time is involved. Can you advise?

This could be improved a little bit by specifying a cell to type in a lambda (or 1/lambda) rather than calculating a mean from the collection of uniform random draws (which will generally be around 0.5). This would also allow the user to make a single draw from RAND() to get a single draw from the exponential with the given lambda.