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 -