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 Jan 28 comment Distribution of the sum of iid Beta-Negative-Binomial random variables Is there a clever way of solving this integral? I tried many ways but always failed. Your help would be greatly appreciated. Dec 6 awarded Supporter Dec 5 comment Distribution of the sum of iid Beta-Negative-Binomial random variables @did Thank you for noticing, I corrected my mistake. If I understand correctly, all that is left is find the solution to the product of the integrals. Dec 5 revised Distribution of the sum of iid Beta-Negative-Binomial random variables deleted 287 characters in body Dec 5 revised Distribution of the sum of iid Beta-Negative-Binomial random variables deleted 287 characters in body Dec 4 awarded Editor Dec 4 revised Distribution of the sum of iid Beta-Negative-Binomial random variables added 330 characters in body Dec 4 comment Distribution of the sum of iid Beta-Negative-Binomial random variables @did: I will add the pmf of the BNB distribution too so it will be more obvious why i tried it this way. Trying to find the characteristic function when using the textbook definition of the pmf has proven to be too hard for me. Dec 4 comment Distribution of the sum of iid Beta-Negative-Binomial random variables @MichaelHardy : That is obviously correct. I will correct that in my question. Dec 4 asked Distribution of the sum of iid Beta-Negative-Binomial random variables Oct 31 comment Sufficient statistic for the Negative-Binomial Distribution $r$ is being estimated in an Maximum-Likelihood Estimation approach. This is what irritates me. The sum can only be the sufficient statistic if $r$ is known but at the same time $r$ is being estimated with MLE. What am I not seeing here? Oct 29 awarded Student Oct 29 asked Sufficient statistic for the Negative-Binomial Distribution