The Excel EXPONDIST 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.

EXPONDIST and EXPON.DIST

In Excel 2010, the Expondist function has been renamed the Expon.Dist function.

Although it has been replaced, the Expondist function is still available in Excel 2010 (stored in the list of compatibility functions), to allow compatibility with earlier versions of Excel.

Basic Description

The Excel Expondist function returns the value of the exponential distribution for a give value of x. The user can specify whether the probability density function or the cumulative distribution function is used.

The syntax of the function is :

EXPONDIST( x, lambda, cumulative )

Where the function arguments are:

The value at which the exponential distribution is to be evaluated (must be ≥ 0)

lambda

The parameter of the distribution

cumulative

A logical argument that specifies the type of distribution to be calculated. This can be either:

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

Expondist Function Examples

Example 1 - Probability Density Function

The chart on the right shows the Exponential Distribution probability density function with the parameter λ set to 0.5, 1, and 2.

If you want to calculate the value of the probability density function with the parameter λ set to 1, at the value x = 0.5, this can be done, using the Excel Expondist function, as follows:

=EXPONDIST( 0.5, 1, FALSE )

This 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 set to 0.5, 1 and 2.

If you want to calculate the value of the cumulative function with the parameter λ set to 1, at the value x = 0.5, this can be done using the Excel Expondist function, as follows:

=EXPONDIST( 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 Expondist function can be found on the Microsoft Office website.

Expondist Function Errors

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

Common Errors

#NUM!

Occurs if either:

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

#VALUE!

Occurs if any of the supplied arguments are not recognised as numeric values

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