ON SIMULATION OF STOCHASTICALLY ORDERED LIFE-LENGTH VARIABLES

  • Authors:

  • Torgny Lindvall

  • Affiliations:

  • Department of Mathematical Statistics, University of Göteborg, 41296 Göteborg, Sweden, E-mail: lindvall@math.chalmers.se

  • Venue:
  • Probability in the Engineering and Informational Sciences
  • Year:
  • 2000

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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).