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ON SIMULATION OF STOCHASTICALLY ORDERED LIFE-LENGTH VARIABLES

Published online by Cambridge University Press:  01 January 2000

Torgny Lindvall
Torgny Lindvall
Affiliation:
Department of Mathematical Statistics, University of Göteborg, 41296 Göteborg, Sweden, E-mail: [email protected]
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Abstract

Let F and G be life-length distributions such that F [D over less-than or equals] G. We solve the following problem: How should (X,Y) be generated in order to maximize [hollow letter P](X = Y), under the conditions X [D over equals] F, Y [D over equals] G, and X ≤ Y? We also find a necessary and sufficient condition for the existence of such a maximal coupling with the property that X and Y are independent, conditioned that X < Y. It is pointed out that using familiar Poisson process thinning methods does not produce (X,Y) which maximizes [hollow letter P](X = Y).

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 14 , Issue 1 , January 2000 , pp. 1 - 7
Copyright
© 2000 Cambridge University Press

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