# The Excel EXPON.DIST Function

Exponential Distribution

The exponential distribution is a continuous probability distribution, which is often used to model the time between events.

The probability density function for the Exponential Distribution is given by the formula:

and the Cumulative Exponential Distribution is given by the formula:

where x is the independant variable and λ is the parameter of the distribution.

## Function Description

For a given value of x and parameter λ the Excel EXPON.DIST function calculates the value of the probability density function or the cumulative distribution function for the exponential distribution.

The function is new in Excel 2010, so is not available in earlier versions of Excel. However, the Expon.Dist function is simply an updated version of the Expondist function, which is available in earlier versions of Excel.

The syntax of the Expon.Dist function is:

EXPON.DIST( x, lambda, cumulative )

where the function arguments are:

x-The value that the exponential distribution is to be evaluated at (must be ≥ 0).
lambda-The parameter of the distribution (must be > 0).
cumulative-

A logical argument that specifies the type of distribution to be calculated. This can have the value TRUE or FALSE, meaning:

 TRUE - Calculate the cumulative distribution function FALSE - Calculate the probability density function

## Expon.Dist Function Examples

### Example 1 - Probability Density Function

Probability Density Exponential Distribution with λ = 0.5, 1 and 2

The above chart on the right shows the probability density functions for the exponential distribution with the parameter λ set to 0.5, 1, and 2.

If you want to calculate value of the function with λ = 1, at the value x=0.5, this can be done using the Excel Expon.Dist function as follows:

=EXPONDIST( 0.5, 1, FALSE )

which gives the result 0.60653066.

### Example 2 - Cumulative Distribution Function

Cumulative Exponential Distribution with λ = 0.5, 1 and 2

The above chart on the right shows the cumulative exponential distribution functions with the parameter λ equal to 0.5, 1 and 2.

If you want to calculate value of the function with λ = 1, at the value x=0.5, this can be done using the Excel Expon.Dist function as follows:

=EXPON.DIST( 0.5, 1, TRUE )

This gives the result 0.39346934.

For further examples of the Excel Expon.Dist function, see the Microsoft Office website.

## Expon.Dist Function Errors

If you get an error from the Excel Expon.Dist function this is likely to be one of the following:

Common Errors
 #NUM! - Occurs if either:The supplied value of x is negativeorThe supplied lambda is ≤ 0. #VALUE! - Occurs if any of the supplied arguments is non-numeric.