Despite a long search I was not able to find a rigorous proof of the fact that a random vector having a multinomial distribution with parameters p (the vector of probabilities) and n (the number of trials) can be written as the sum of n independent random vectors all having a multinomial distribution with parameters p and 1. Can anyone suggest where to look?
Proof concerning the multinomial distribution
4
$\begingroup$
probability-distributions
-
0Use characteristic function to prove it. – 2012-09-28
-
2Actually, I suspect that the result above is needed to derive the characteristic function, so it would be circular. – 2012-09-28