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Oct 28, 2020 at 19:01 vote accept William
Dec 25, 2019 at 10:47 comment added William @losifPinelis could you look at this question: mathoverflow.net/questions/346660/…
Nov 22, 2019 at 21:33 comment added William I used Matlab to draw the distribution of the above summation. Not only that, I averaged its mean and variance and put it in a gamma function and it almost identical to the simulated one.
Nov 22, 2019 at 21:29 comment added Iosif Pinelis @AymenKareem : How do you it works only for very large $N,K$? And what do you mean by "works"? Also, why would you prefer a gamma approximation to a normal one? In fact, I don't remember ever seeing approximations by a gamma distribution.
Nov 22, 2019 at 5:53 comment added William How do I know which distribution is the best approximate for a certain situation?
Nov 22, 2019 at 4:49 comment added William Thanks losif, it works only when N, K are very large (N=1000, K=10). How about Gamma distribution? Can the above summation in the question be approximated as Gamma?
Nov 22, 2019 at 2:29 history answered Iosif Pinelis CC BY-SA 4.0