The Excel GAMMA.DIST Function

Related Function:
GAMMA.INV
Gamma Distribution Function

The Gamma Distribution is frequently used to provide probabilities for sets of values that may have a skewed distribution, such as queuing analysis.

The function is explained in detail on the Wikipedia Gamma Distribution page.

Basic Description

For a set of supplied parameters, the Excel Gamma.Dist function calculates the value of either the cumulative distribution or the probability density function for the Gamma Distribution.

The Gamma.Dist function is new in Excel 2010 and so is not available in earlier versions of Excel. However, the function is simply a new version of the Gammadist function, that is available in earlier versions of Excel.

The syntax of the Gamma.Dist function is:

GAMMA.DIST( x, alpha, beta, cumulative )

where the function arguments are:

x-A positive value at which you want to evaluate the function.
alpha-A parameter of the distribution.
beta-

A parameter of the distribution.

(Note: if beta=0, then the Standard Gamma distribution is calculated).
cumulative-

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

TRUE-cumulative distribution function;
FALSE-probability density function.


Gamma.Dist Function Examples

Example 1 - Probability Density Function

Plot of the Probability Density Gamma Distribution with α = 3 and β = 2
Gamma Probability Density Distribution with α=3 & β=2

The above chart on the right shows the probability density function for the gamma distribution with α = 3 and β = 2.

The value of this function for a selected value of x can be calculated by the Excel Gamma.Dist function. For example, the function value at x = 6 is given by:

=GAMMA.DIST( 6, 3, 2, FALSE )

which gives the result 0.112020904.


Example 2 - Cumulative Distribution Function

Plot of the Cumulative Gamma Distribution Function with α = 3 and β = 2
Cumulative Gamma Distribution Function with α=3 & β=2

The above chart on the right shows the Cumulative Gamma Distribution with α = 3 and β = 2.

If you want to calculate the value of this function at x = 6, this can be done using the Excel Gamma.Dist function, as follows:

=GAMMA.DIST( 6, 3, 2, TRUE )

This gives the result 0.576809919.


Further details and examples of the Excel Gamma.Dist function are provided on the Microsoft Office website.


Gamma.Dist Function Errors

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

Common Errors
#NUM!-

Occurs if either:

  • The supplied value of x is < 0;
  • The supplied value of alpha ≤ 0 or beta ≤ 0.
#VALUE!-

Occurs if either:

  • Any of the supplied arguments, x, alpha or beta are not recognised as numeric values;
  • The supplied value of cumulative is not recognised as a logical or a numeric value.