GAMMADIST 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

GAMMADIST(x,alpha,beta,cumulative)

X     is the value at which you want to evaluate the distribution.

Alpha     is a parameter to the distribution.

Beta     is a parameter to the distribution. If beta = 1, GAMMADIST returns the standard gamma distribution.

Cumulative     is a logical value that determines the form of the function. If cumulative is TRUE, GAMMADIST returns the cumulative distribution function; if FALSE, it returns the probability density function.

Remarks

  • If x, alpha, or beta is nonnumeric, GAMMADIST returns the #VALUE! error value.

  • If x < 0, GAMMADIST returns the #NUM! error value.

  • If alpha ≤ 0 or if beta ≤ 0, GAMMADIST 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, GAMMADIST returns the exponential distribution with:

    Equation

  • For a positive integer n, when alpha = n/2, beta = 2, and cumulative = TRUE, GAMMADIST returns (1 - CHIDIST(x)) with n degrees of freedom.

  • When alpha is a positive integer, GAMMADIST is also known as the Erlang distribution.

Example

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

How to copy an example

  1. Create a blank workbook or worksheet.

  2. Select the example in the Help topic.

    Note   Do not select the row or column headers.

    Selecting an example from Help

    Selecting an example from Help

  3. Press CTRL+C.

  4. In the worksheet, select cell A1, and press CTRL+V.

  5. 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.

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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)

=GAMMADIST(A2,A3,A4,FALSE)

Probability gamma distribution with the terms above (.03263913)

=GAMMADIST(A2,A3,A4,TRUE)

Cumulative gamma distribution with the terms above (0.068094)

Applies To: Excel 2007



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