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Optimal lower bounds for bivariate probabilities

Part of: Distribution theory - Probability

Published online by Cambridge University Press:  01 July 2016

Tuhao Chen
Tuhao Chen*
Affiliation:
University of Sydney, Australia
*
∗ Postal address: Dept. of Mathematics and Statistics, McMaster University, 1280 Main St. West, Hamilton, Ontario, Canada L8S 4K1.
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Abstract

This paper deals with existence of bivariate Fréchet optimal lower bounds for two sets of events, and provides a practical approach to find this kind of bound. The main device used is linear programming ideas, coupled with construction of probability spaces. The highlight of this paper is that perturbation terms in the optimization process, even when a tie occurs, are not necessary in this practical implementation.

Keywords

Fréchet optimalitylinear programmingprobability spaceiterationoptimizationcyclingperturbation

MSC classification

Primary: 60E15: Inequalities; stochastic orderings
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 30 , Issue 2 , June 1998 , pp. 476 - 492
Copyright
Copyright © Applied Probability Trust 1998 

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