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Random variables with maximum sums

Published online by Cambridge University Press:  01 July 2016

Ludger Rüschendorf*
Affiliation:
University of Freiburg
*
Postal address: Institut für Mathematische Stochastik, Universität Freiburg, Hebelstr. 27, 7800 Freiburg, W. Germany.

Abstract

Motivated by a problem in PERT networks we consider the question of construction of random variables with maximum sums when the marginals are fixed.

Type
Research Article
Copyright
Copyright © Applied Probability Trust 1982 

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References

Gaffke, N. and Rüschendorf, L. (1981) On a class of extremal problems in statistics. Math. Operationsforsch. Statist. Ser. Optimization 12, 123136.Google Scholar
Lai, T. L. and Robbins, H. (1978) A class of dependent random variables and their maxima. Z. Wahrscheinlichkeitsth. 42, 89111.Google Scholar
Mallows, C. L. (1969) Extrema of expectations of uniform order statistics. SIAM Review 11, 410411.Google Scholar
Meilijson, I. and Nádas, A. (1919) Convex majorization with an application to the length of critical paths. J. Appl. Prob. 16, 671677.Google Scholar
Robillard, P. and Trahan, M. (1977) The completion time of PERT networks. Operat. Res. 25, 1529.CrossRefGoogle Scholar
Rockafellar, R. T. (1970) Convex Analysis. Princeton University Press.Google Scholar
Rüschendorf, L. (1980) Solution of a statistical optimization problem by rearrangement methods. Metrika. Google Scholar
Rüschendorf, L. (1981) Sharpness of Fréchet-bounds. Z. Wahrscheinlichkeitsth. 57, 293302.Google Scholar
Strassen, V. (1965) The existence of probability measures with given marginals. Ann. Math. Statist. 36, 423438.Google Scholar