GAMMADIST

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:

  

  The standard gamma distribution is:

  

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

  

• 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)