Parametric Schur Convexity and Arrangement Monotonicity Properties of Partial Sums

M. Shaked, Jevaveerasingam Shanthikumar and Y. L. Tong

Journal of Multivariate Analysis, 1995, vol. 53, issue 2, 293-310

Abstract: 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.

Date: 1995
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