TY - JOUR

T1 - Sharp bounds on the largest of some linear combinations of random variables with given marginal distributions

AU - Meilijson, Isaac

PY - 1991/1

Y1 - 1991/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84971985362&partnerID=8YFLogxK

U2 - 10.1017/S0269964800001856

DO - 10.1017/S0269964800001856

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AN - SCOPUS:84971985362

SN - 0269-9648

VL - 5

SP - 1

EP - 14

JO - Probability in the Engineering and Informational Sciences

JF - Probability in the Engineering and Informational Sciences

IS - 1

ER -