I have distilled an error analysis problem into the following:
I have a multinomial distribution, $X$, consisting of $n$ independent trials where each trial takes on the values $\{0,1,\ldots,k-1\}$ with uniform probability of $\frac{1}{k}$.
Now I am interested in finding the distribution of the sum of all the outcomes in the $n$ trials, but not sure how to approach the problem. I suspect it has something to do with partition functions. Would be glad if the relevant probability distribution function in MATLAB could also be pointed out.