CHARACTERIZATIONS OF THE GAMMA DISTRIBUTION BY INDEPENDENCE PROPERTY OF RANDOM VARIABLES

• 발행기관: 충청수학회
• 저자명: Hyun-Woo Jin Min-Young Lee
• 간행물 정보: 『Journal of the Chungcheong Mathematical Society』Volume 27, No. 2, 157~163쪽, 전체 7쪽
• 주제분류: 자연과학 > 자연과학일반
• 파일형태: PDF
• 발행일자: 2014.05.30

영문 초록

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.

목차

1. Introduction

2. Results

3. Proofs