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Parametric Schur Convexity and Arrangement Monotonicity Properties of Partial Sums

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  • Shaked, M.
  • Shanthikumar, J. G.
  • Tong, Y. L.

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.

Suggested Citation

  • Shaked, M. & Shanthikumar, J. G. & Tong, Y. L., 1995. "Parametric Schur Convexity and Arrangement Monotonicity Properties of Partial Sums," Journal of Multivariate Analysis, Elsevier, vol. 53(2), pages 293-310, May.
    • Handle: RePEc:eee:jmvana:v:53:y:1995:i:2:p:293-310
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    Cited by:

    1. Wei-Feng Xia & Xiao-Hui Zhan & Gen-Di Wang & Yu-Ming Chu, 2012. "Some properties for a class of symmetric functions with applications," Indian Journal of Pure and Applied Mathematics, Springer, vol. 43(3), pages 227-249, June.
    2. Ma, Chunsheng, 2000. "ISO* Property of Two-Parameter Compound Poisson Distributions with Applications," Journal of Multivariate Analysis, Elsevier, vol. 75(2), pages 279-294, November.
    3. Shaked, Moshe & Shanthikumar, J. George, 1997. "Supermodular Stochastic Orders and Positive Dependence of Random Vectors," Journal of Multivariate Analysis, Elsevier, vol. 61(1), pages 86-101, April.

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