CHARACTERIZATIONS OF THE GAMMA DISTRIBUTION BY INDEPENDENCE PROPERTY OF RANDOM VARIABLES

Abstract

Let {Xi , 1 ≤ i ≤ n} be a sequence of i.i.d. sequence of positive random variables with common absolutely continuous cumulative distribution function F (x) and probability density function f (x) and E(X 2) < ∞. The random variables X + Y and (X−Y )2 (X+Y )2 are independent if and only if X and Y have gamma disi=1(Xi)2 (Sn)2

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