In reply to Kaushik Bhattacharjee.

No, sorry. I have written several articles about MLE estimation of parameters for fitting distributions to data. See "Two ways to compute maximum likelihood estimates in SAS." I do not have any experience working with the SGT, but fitting a five-parameter family will probably require a lot of data. As for simulation, it looks like (via Google) it involves the incomplete beta function or the incomplete gamma function.