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GAMMA.DIST function: Description, Usage, Syntax, Examples and Explanation

What is GAMMA.DIST function in Excel?

GAMMA.DIST function is one of Statistical functions in Microsoft Excel that returns the gamma distribution. You can use this function to study variables that may have a skewed distribution. The gamma distribution is commonly used in queuing analysis.

Syntax of GAMMA.DIST function

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

The GAMMA.DIST function syntax has the following arguments:

  • X:  The value at which you want to evaluate the distribution.
  • Alpha: A parameter to the distribution.
  • Beta: A parameter to the distribution. If beta = 1, GAMMA.DIST returns the standard gamma distribution.
  • Cumulative:  A logical value that determines the form of the function. If cumulative is TRUE, GAMMA.DIST returns the cumulative distribution function; if FALSE, it returns the probability density function.

GAMMA.DIST formula explanation

  • If x, alpha, or beta is nonnumeric, GAMMA.DIST returns the #VALUE! error value.
  • If x < 0, GAMMA.DIST returns the #NUM! error value.
  • If alpha ≤ 0 or if beta ≤ 0, GAMMA.DIST returns the #NUM! error value.
  • The equation for the gamma probability density function is:EquationThe standard gamma probability density function is:Equation
  • When alpha = 1, GAMMA.DIST returns the exponential distribution with:Equation
  • For a positive integer n, when alpha = n/2, beta = 2, and cumulative = TRUE, GAMMA.DIST returns (1 – CHISQ.DIST.RT(x)) with n degrees of freedom.
  • When alpha is a positive integer, GAMMA.DIST is also known as the Erlang distribution.

Example of GAMMA.DIST function

Steps to follow:

1. Open a new Excel worksheet.

2. Copy data in the following table below and paste it in cell A1

Note: For formulas to show results, select them, press F2 key on your keyboard and then press Enter.

You can adjust the column widths to see all the data, if need be.

Data Description
10.00001131 Value at which you want to evaluate the distribution
9 Alpha parameter to the distribution
2 Beta parameter to the distribution
Formula Description Result
=GAMMA.DIST(A2,A3,A4,FALSE) Probability density using the x, alpha, and beta values in A2, A3, A4, with FALSE cumulative argument. 0.032639
=GAMMA.DIST(A2,A3,A4,TRUE) Cumulative distributuion using the x, alpha, and beta values in A2, A3, A4, with TRUE cumulative argument. 0.068094

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