PARAMETRIC SCHUR CONVEXITY AND ARRANGEMENT MONOTONICITY PROPERTIES OF PARTIAL-SUMS

被引:30
作者
SHAKED, M
SHANTHIKUMAR, JG
TONG, YL
机构
[1] UNIV CALIF BERKELEY,BERKELEY,CA
[2] GEORGIA INST TECHNOL,ATLANTA,GA
关键词
STOCHASTIC ORDERING; LIKELIHOOD RATIO ORDERING; MAJORIZATION AND SCHUR-CONVEXITY; RELIABILITY THEORY; STOCHASTIC CONVEXITY;
D O I
10.1006/jmva.1995.1038
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
Studying the joint distributional properties of partial sums of independent random variables, we obtain stochastic analogues of some simple deterministic results from the theory of majorization, Schur-convexity, and arrangement monotonicity. More explicitly, let X(i)(theta(i)), i=1, ..., n, be independent random variables such that the distribution of X(i)(theta(i)) is determined by the value of theta(i). Let S(theta) = (X(1)(theta(1)), X(1)(theta(1)) + X(2)(theta(2)), ..., Sigma(i=1)(n) X(i)(theta(i))). We give sufficient conditions on f:R(n) --> R and on {X(i)(theta), theta is an element of Theta} under which f(S(theta)) have some stochastic arrangement monotonicity and stochastic Schur-convexity properties. (C) 1995 Academic Press, Inc.
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页码:293 / 310
页数:18
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