Thank you, Dr Jochen Wilhelm, for pointing me.

Minimization of the absolute distance between the empirical and the estimated distribution is based on Kolmogorov-Smirnov(KS) criterion, and the method of minimization of squared difference between the empirical and the estimated distribution is based on Cramér–von Mises (CVM) criterion. 

KS approach is more aware of the centre of distribution, however, CVM aware on the whole space. Both of the criteria exhibit diverging degrees of test bias in some situations. The KS has more power against deviations in the middle, but not at all. Also, as I found, it is computationally easy.

Please correct me, If I am going wrong.

Thankyou

http://stats.stackexchange.com/questions/201434/2-sample-kolmogorov-smirnov-vs-anderson-darling-vs-cramer-von-mises

# R-code:

# using the generalized gamma distribution as defined in the

# package flexsurv (install this package if not yet done:

# install.packages("flexsurv") )

library("flexsurv")

# setting some arbitrary values for the parameters:

m = log(5)

s = log(1.2)

Q = 1

# and generate some random values according to this model:

r = rgengamma(100, mu=m, sigma=s, Q=1)

# just to have a look: the histogram of the values:

H

Once you have the distribution loaded from {flexsurv} you should also be able to use the fitdist() function, from the package {fitdistrplus}.

Nice tip, thanks.

fitdist(r, "gengamma", start=list(mu=log(4),sigma=log(1.5),Q=0) )

in fact gives very similar results and additionally some information about the uncertainty and correlation of the parameter estimates. This package also provides some convenient functions to produce plots comparing data and fitted model.

These are fantastic answers!

Thanks a lot, guys! :)

Glad it worked! I've only used it for ex-gaussian so far so it's good to know it worked for this one too!

It works! :o)

In fact, I am also interested in the estimate of the mathematical expectation of r after we used fitdistr. Any ideas of how this could be quickly accomplished?

Thanks!

The expected value as a function of the parameters of the generalized gamma distribution is listed in the Wikipedia article:

https://en.wikipedia.org/wiki/Generalized_gamma_distribution

The problem is that this article uses a different parametrization, but in the help of the package flexsurf you can find how these parameters van be calculated from (m(u), s(igma), Q).

I see - thanks! Perhaps, there's a general approach to find the estimate of the mean if we've found the distribution using the fitdistr function.

The general approach is to integrate x*p(x) over x, where p() is the probabiliy density.

https://en.wikipedia.org/wiki/Expected_value#Univariate_continuous_random_variable

Thanks a lot! I'll try implement this approach.

Minimization the ks-distance is better to fit a probability distribution for data, rather than the sum of the square of differences. So error function should be,

errf

Arun, could you give me a reason or a reference for that?

Thank you, Dr Jochen Wilhelm, for pointing me.

Minimization of the absolute distance between the empirical and the estimated distribution is based on Kolmogorov-Smirnov(KS) criterion, and the method of minimization of squared difference between the empirical and the estimated distribution is based on Cramér–von Mises (CVM) criterion. 

KS approach is more aware of the centre of distribution, however, CVM aware on the whole space. Both of the criteria exhibit diverging degrees of test bias in some situations. The KS has more power against deviations in the middle, but not at all. Also, as I found, it is computationally easy.

Please correct me, If I am going wrong.

Thankyou

http://stats.stackexchange.com/questions/201434/2-sample-kolmogorov-smirnov-vs-anderson-darling-vs-cramer-von-mises

Thanks a lot for your answers!

At present I'm trying to figure out how it would be better to construct an R code to find an estimate of the mean of a random variable that follows the general gamma distribution. Any thoughts on this matter would be highly appreciated!