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GAMMADIST

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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 mass 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 distribution is:

    Cc767571.ZA060511461033(en-us,TechNet.10).gif

    The standard gamma distribution is:

    Cc767571.ZA060511471033(en-us,TechNet.10).gif

  • When alpha = 1, GAMMADIST returns the exponential distribution with:

    Cc767571.ZA060511481033(en-us,TechNet.10).gif

  • 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

X

Alpha

Beta

Formula

Description (Result)

10

9

2

=GAMMADIST([X],[Alpha],[Beta],FALSE)

Probability gamma distribution of the arguments (0.032639)

10

9

2

=GAMMADIST([X],[Alpha],[Beta],TRUE)

Cumulative gamma distribution of the arguments (0.068094)

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