Monday, June 2, 2008

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.