You must must first fit your rainfall data (means estimate the parameters of the distribution). You can do that for instance with the fitdistrplus package in R. Then the Lilliefors test must be used to measure the chances (probability) that your fitted distribution really follows the gamma law

Dear Jefferson,

you could use the Kolmogorov-Smirnov minimum distance estimator from package distrMod to estimate the parameters and then apply function ks.test as shown in the examples section of the help page of ks.test.

The Lilliefors test is a specialisation of the Kolmogorov-Smirnov test to the normal distribution.

In testing for distributions the sample size is a crucial point. Using function qqplot of package distrMod would be an alternative to testing.

Best,

Matthias

Dear Matthias,

I found in the literature that we need to use the Lilliefors test for incomplete gamma distribution, cause I can't use the same data I used to estimate the two parameters (alfa and beta) for fit the function according to some authors. So, I thank you for the advice me about Normal distribution to fit the data, but I'm quite sure I need to use Lilliefors test for gamma.

Best,

Jefferson

Dear Jefferson,

this was a misunderstanding. I meant that you could estimate the parameters of the gamma distribution by means of the Kolmogorov-Smirnov minimum distance estimator using R package distrMod and then use these parameters in combination with function ks.test to perform the Kolmogorov-Smirnov test.

Best,

Matthias