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On explicit and Fréchet-optimal lower bounds

Part of: Distribution theory - Probability

Published online by Cambridge University Press:  14 July 2016

Eugene Seneta  and
John Tuhao Chen
Eugene Seneta*
Affiliation:
University of Sydney
John Tuhao Chen*
Affiliation:
Bowling Green State University
*
∗ Postal address: School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia. Email address: eseneta@maths.usyd.edu.au
∗∗ Postal address: Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH 43403, USA.
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Abstract

Ease of computation of Fréchet-optimal lower bounds, given numerical values of the binomial moments Sij, i, j = 1, 2, is demonstrated. A sufficient condition is given for an explicit bivariate bound of Dawson-Sankoff structure to be Fréchet optimal. An example demonstrates that in the bivariate case even the multiplicative structure of the Sij does not guarantee a Dawson-Sankoff structure for Fréchet-optimal bounds. A final section is used to illuminate the nature of Fréchet optimality by using generalized explicit bounds. This note is a sequel to both Chen and Seneta (1995) and Chen (1998).

Keywords

Fréchet optimalityexplicit boundslinear programmingDawson-Sankoff structureprobability spaceproduct space

MSC classification

Primary: 60E15: Inequalities; stochastic orderings
Type
Research Papers
Information
Journal of Applied Probability , Volume 39 , Issue 1 , March 2002 , pp. 81 - 90
Copyright
Copyright © Applied Probability Trust 2002 

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Footnotes

Work done in part at the University of Sydney.

References

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