Thanks for the reply.
I also got the same integral:
but didn't know (and still don't) what do with it
Actually, I'm trying to get goodness-of-fit of the empyrical data to a GGDs with different shape parameters c.
The Kolmogorov-Smirnov test needs the empyrical

and the distribution CFD

.
In Matlab (and in general) it is easy to find the empyrical CDF of the given data and evaluate it at each sample, but how do I get the value of the GGD CDF?