Gamma Distribution

This distribution includes the Erlang and Chi-Square distributions as special cases.

Parameters: Location (L), Scale (s), Shape ( beta)

Formula:

Formula for gamma distribution

where gamma is the gamma function.

Note:

Some textbook Gamma formulas use:

s equals 1 divided by lamda

Method 1:

When beta is less than 1, Vaduva’s rejection from a Weibull density.

When beta is greater than 1, Best’s rejection from a t density with 2 degrees of freedom.

When beta = 1, inverse transformation.

Method 2: Rational Fraction Approximation method with a Newton Polish step

Comment: This method is used instead of Method 1 when Latin Hypercube sampling is in effect.