The Excel EXPON.DIST Function

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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.

Basic 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 a renamed version of the Expondist function, that is available in earlier versions of Excel.

The syntax of the function is :

EXPON.DIST( x, lambda, cumulative )

where the function arguments are:

A positive number, denoting the value that the exponential distribution is to be evaluated at

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

The 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.

Plot of the Exponential Distribution Probability Density Function with the Parameter lambda set to 0.5, 1 and 2

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

Example 2 - Cumulative Distribution Function

The 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.

Plot of the Cumulative Exponential Distribution with the Parameter lambda set to 0.5, 1 and 2

Cumulative Exponential Distribution with λ = 0.5, 1 and 2

Further examples of the Excel Expon.Dist function can be found on the Microsoft Office website.

Expon.Dist Function Errors

The following table lists the reasons for the most commonly encountered Excel errors, when using the Excel Expon.Dist function :

Common Errors

#NUM!

Occurs if either:

	-	the supplied value of x is negative
or
	-	the supplied value of lambda is ≤ 0

#VALUE!

Occurs if any of the supplied arguments are not non-numeric

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