Statistical - GAMMA.DIST Function

Description

The 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)

Arguments

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

A logical value that determines the form of the function.

If cumulative is TRUE, GAMMA.DIST returns the cumulative distribution function.

If cumulative is FALSE, GAMMA.DIST returns the probability density function.

 Required

Notes

  • The equation for the gamma probability density function is −

    $$f\left (x,\alpha ,\beta \right )=\frac{1}{\beta ^a\Gamma \left ( \alpha \right )}x^{a-1}e^-\frac{N}{\beta }$$

  • The standard gamma probability density function is −

    $$f\left (x,\alpha \right )=\frac{x^{a-1}e^N}{\Gamma \left ( \alpha \right )}$$

  • When alpha = 1, GAMMA.DIST returns the exponential distribution with −

    $$\lambda =\frac{1}{\beta }$$

  • 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.

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

  • If the specified value of cumulative is not recognized as a logical or a numeric value, 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.

Applicability

Excel 2010, Excel 2013, Excel 2016

Example

Gamma.Dist Function
advanced_excel_statistical_functions.htm
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