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Multivariate product-type lower bounds

Part of: Distribution theory Distribution theory - Probability

Published online by Cambridge University Press:  14 July 2016

Henry W. Block  and
Tuhao Chen
Henry W. Block*
Affiliation:
University of Pittsburgh
Tuhao Chen
Affiliation:
University of Pittsburgh
*
∗ Postal address: Department of Statistics, University of Pittsburgh, Pittsburgh, PA 15260, USA.
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Abstract

Univariate probability inequalities have received extensive attention. It has been shown that under certain conditions, product-type bounds are valid and sharper than summation-type bounds. Although results concerning multivariate inequalities have appeared in the literature, product-type bounds in a multivariate setting have not yet been studied. This note explores an approach using graph theory and linear programming techniques to construct product-type lower bounds for the probability of the intersection among unions of k sets of events.

Keywords

multivariate inequalityspanning treepositive dependenceproduct-type boundlinear programmingbivariate Frechét optimal boundMTP2

MSC classification

Primary: 60E15: Inequalities; stochastic orderings
Secondary: 62E17: Approximations to distributions (nonasymptotic)
Type
Research Papers
Information
Journal of Applied Probability , Volume 38 , Issue 2 , June 2001 , pp. 407 - 420
Copyright
Copyright © Applied Probability Trust 2001 

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Footnotes

∗∗

Current address: Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH 43403, USA. Email address: jchen@bgnet.bgsu.edu

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