Gamma distribution

Returns either the cumulative Gamma distribution or the probability density of a random variable. This function is used in queueing analysis to study variables that may have a skewed distribution.

Syntax

GammaDistribution <Cumulative> (x, Alpha, Beta)

Where:

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

Alpha is a distribution parameter.

Beta is a distribution parameter.

Cumulative is a logical value that determines the form of the function:

• If Cumulative=0 (default), it returns the cumulative distribution.
• If Cumulative=1, it returns the probability density.

Expression

The expression for the standard gamma distribution is:

If alpha = 1, this function returns the exponential distribution as:

Usage Notes

When alpha > 0, this function is also known as the Erlang distribution.

The following conditions are invalid:

• Either alpha or beta is nonnumeric
• Either alpha £ 0 or beta £ 0
• x < 0