GAMMA.DIST function

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

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

The GAMMA.DIST function syntax has the following arguments (argument: A value that provides information to an action, an event, a method, a property, a function, or a procedure.):

  • X     Required. The value at which you want to evaluate the distribution.
  • Alpha     Required. A parameter to the distribution.
  • Beta     Required. A parameter to the distribution. If beta = 1, GAMMA.DIST returns the standard gamma distribution.
  • Cumulative     Required. 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.

Remarks

  • 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:

Equation

The 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

The example may be easier to understand if you copy it to a blank worksheet.

ShowHow do I copy an example?

  1. Select the example in this article. If you are copying the example in Excel Online, copy and paste one cell at a time.
    Important: Do not select the row or column headers.

Selecting an example from Help

Selecting an example from Help

  1. Press CTRL+C.
  2. Create a blank workbook or worksheet.
  3. In the worksheet, select cell A1, and press CTRL+V. If you are working in Excel Online, repeat copying and pasting for each cell in the example.
    Important: For the example to work properly, you must paste it into cell A1 of the worksheet.
  4. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

After you copy the example to a blank worksheet, you can adapt it to suit your needs.

 
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A B
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 gamma distribution with the terms above (.03263913)
=GAMMA.DIST(A2,A3,A4,TRUE) Cumulative gamma distribution with the terms above (0.068094)
 
 
Applies to:
Excel 2010, Excel Web App, SharePoint Online for enterprises, SharePoint Online for professionals and small businesses