Parametric Schur convexity and arrangement monotonicity properties of partial sums
Parametric Schur convexity and arrangement monotonicity properties of partial sums
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DOI：
10.1006/jmva.1995.1038
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发表时间：
1995-05
影响因子：
1.6
通讯作者：
M. Shaked;J. Shanthikumar;Y. Tong
中科院分区：
文献类型：
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作者：
M. Shaked;J. Shanthikumar;Y. Tong
研究了独立随机变量部分和的联合分布性质，从多数化理论、舒尔-凸性理论和排列单调性理论中得到了一些简单确定性结果的随机类似。更明确地说，令Xi([θ]i), i =1，…， n为独立随机变量，使得Xi（[theta]i）的分布由[theta]i的值决定。让年代((θ))= (X1((θ)1),X1(1)(θ)+ X2((θ)2),…， [σ]ni = 1Xi([θ]i))。给出了f: n—>和{Xi([theta])， [theta][集合隶属度，变量][theta]}上f（S([theta])）具有随机排列单调性和随机舒尔-凸性的充分条件。
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 Xi([theta]i), i =1, ..., n, be independent random variables such that the distribution of Xi([theta]i) is determined by the value of [theta]i. Let S([theta]) = (X1([theta]1), X1([theta]1) + X2([theta]2), ..., [Sigma]ni = 1Xi([theta]i)). We give sufficient conditions on f : n --> and on {Xi([theta]), [theta] [set membership, variant] [Theta]} under which f(S([theta])) have some stochastic arrangement monotonicity and stochastic Schur-convexity properties.