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Sharp Bounds on the Largest of some Linear Combinations of Random Variables with Given Marginal Distributions

Published online by Cambridge University Press:  27 July 2009

Isaac Meilijson
Isaac Meilijson
Affiliation:
School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences Tel Aviv University, Tel Aviv, Israel
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Abstract

Let X be a random vector and A a matrix. Let M be the maximal coordinate of the vector AX. For given marginal distributions of the coordinates of X, we present sharp bounds on the expectations of convex increasing functions of M. We derive joint distributions of X that achieve some of these bounds, and under these “worst case” distributions we study the joint distribution of M and the index of the largest coordinate of AX. Some possible applications are PERT network analysis and design of experiments.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 5 , Issue 1 , January 1991 , pp. 1 - 14
Copyright
Copyright © Cambridge University Press 1991

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