학술저널
CHARACTERIZATIONS OF THE GAMMA DISTRIBUTION BY INDEPENDENCE PROPERTY OF RANDOM VARIABLES
- 충청수학회
- Journal of the Chungcheong Mathematical Society
- Volume 27, No. 2
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2014.05157 - 163 (7 pages)
- 2
Let fXi ; 1 · i · ng be a sequence of i.i.d. sequence of positive random variables with common absolutely continuous cu-mulative distribution function F(x) and probability density func-tion f(x) and E(X2) < 1. The random variables X + Y and(X¡Y )2(X+Y )2 are independent if and only if X and Y have gamma dis- tributions. In addition, the random variables Sn andPmi=1(Xi)2(Sn)2with Sn =Pni=1 Xi are independent for 1 · m < n if and only if Xi has gamma distribution for i = 1; ¢ ¢ ¢ ; n.
1. Introduction
2. Results
3. Proofs
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