CHARACTERIZATIONS OF GAMMA DISTRIBUTION

Abstract

Let X1, · · · , Xn be nondegenerate and positive independent identically distributed(i.i.d.) random variables with common absolutely continuous distribution function F (x) and E(X 2) < ∞. The random variables X1 + · · · + Xn and X1+···+Xm are independent for 1 ≤ m < n if and only X1+···+Xn if X1, · · · , Xn have gamma distribution.

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