Gamma Distribution CDF

See http://groups.google.com/group/ampl/browse_thread/thread/10861bd79114dfec. In GAMS we have the GAMMAREG function (see http://www.gams.com/~erwin/specfun.pdf) so no need to program this yourself using external functions.

The Gamma CDF from http://en.wikipedia.org/wiki/Gamma_distribution denoted by F(x;k,θ) with

• scale parameter θ
• shape parameter k
• mean: k·θ
• variance: k·θ²

can be expressed in GAMS by:

F(x;k,θ) = GAMMAREG(x/θ,k)

Both first and second derivatives are available for solvers calling this function.