Related Function:

The GAMMA.DIST function returns the value of either the cumulative distribution or the probability density function for the Gamma distribution.

  • This function was introduced in Excel 2010 and so is not available in earlier versions.
  • The GAMMA.DIST function replaces the GAMMADIST function included in earlier versions of Excel.

Syntax

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

Arguments

Argument Description
x A positive value at which you want to evaluate the function
alpha A parameter of the distribution
beta A parameter of the distribution – 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

Examples

  A B C D
1 Data Description    
2 12.0133112 Value at which to evaluate the distribution
3 8 Alpha parameter to the distribution
4 3 Beta parameter to the distribution
5        
6 Formula Result Notes
7 =GAMMA.DIST(A2,A3,A4,FALSE) 0.019913 Probability density using the x, alpha, and beta values in A2, A3, A4, with FALSE cumulative argument
8 =GAMMA.DIST(A2,A3,A4,TRUE) 0.051398 Cumulative distributuion using the x, alpha, and beta values in A2, A3, A4, with TRUE cumulative argument

Common Function Error(s)

Problem What went wrong
#VALUE! Occurs if either:

  any of the supplied arguments, xalpha or beta are not recognized as numeric values
  the supplied value of cumulative is not recognized as a logical or a numeric value
#NUM! Occurs if either:

  the supplied value of x is < 0
  the supplied value of alpha ≤ 0 or beta ≤ 0

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

The equation for the gamma probability density function is:    

    \[    f(x;k,\theta) = \frac 1{\theta^k \Gamma (k) } x^{k-1} e^{\frac x{\theta} }    \]

The formula for the cumulative distribution function is the regularized gamma function:

    \[    f(x;k) = \frac {x^{k-1} e^{-n} }{\Gamma(k)}    \]

See Wikipedia for more information on Gamma Distribution.