Sharp bounds on the largest of some linear combinations of random variables with given marginal distributions

Isaac Meilijson*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)1-14
Number of pages14
JournalProbability in the Engineering and Informational Sciences
Volume5
Issue number1
DOIs
StatePublished - Jan 1991

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