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Max-infinite divisibility and multivariate total positivity

Part of: Distribution theory - Probability Multivariate analysis

Published online by Cambridge University Press:  14 July 2016

Abdulhamid A. Alzaid  and
Frank Proschan
Abdulhamid A. Alzaid*
Affiliation:
King Saud University
Frank Proschan*
Affiliation:
Florida State University
*
∗ Postal address: Department of Statistics and Operations Research, King Saud University, P.O. Box 2455, Riyadh-11451, Saudi Arabia.
∗∗ Postal address: Department of Statistics, Florida State University, Tallahassee, FL 32306-3033, USA.
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Abstract

The concept of max-infinite divisibility is viewed as a positive dependence concept. It is shown that every max-infinitely divisible distribution function is a multivariate totally positive function of order 2 (MTP2). Inequalities are derived, with emphasis on exchangeable distributions. Applications and examples are given throughout the paper.

Keywords

EXCHANGEABLE RANDOM VARIABLESMULTIVARIATE EXTREMAL PROCESSRELIABILITYSERIES SYSTEMPARALLEL SYSTEMEXTREME VALUE DISTRIBUTIONMULTIVARIATE DEPENDENCEINEQUALITIESMIN-INFINITE DIVISIBILITY

MSC classification

Primary: 60E07: Infinitely divisible distributions; stable distributions
Secondary: 62H20: Measures of association (correlation, canonical correlation, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 31 , Issue 3 , September 1994 , pp. 721 - 730
Copyright
Copyright © Applied Probability Trust 1994 

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Footnotes

Research partially supported by Grant AFOSR 91–0048.

Research supported by Grant AFOSR 91-0048.

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