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Positive Dependence of Exchangeable Sequences

Published online by Cambridge University Press:  20 November 2018

R. M. Burton  and
A. R. Dabrowski
R. M. Burton
Affiliation:
Department of Mathematics, Oregon State University, Corvallis, Oregon 97331 U.S.A.
A. R. Dabrowski
Affiliation:
Department of Mathematics, University of Ottawa, Ottawa, Ontario, K1N6N5
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Abstract

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Infinite sequences of exchangeable binary random variables have strong positive dependence properties; in particular, we show they are strong FKG. If the infinite exchangeable sequence is allowed to have multiple values this is no longer true. Positive dependence conditions such as association still have natural application in this context. We establish necessary and sufficient conditions for an infinite exchangeable sequence to be associated. This result shows that exchangeable Polyà urn processes are associated. We also establish necessary and sufficient conditions for finite exchangeable sequences to be weakly associated. The match set distribution of a random permutation has recently been shown to be associated by an extensive analysis of cases. Our result easily yields the weak association of such distributions.

Keywords

60E1560K99associationexchangeableFKGmatch set distributionsPolyă urn models
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 44 , Issue 4 , 01 August 1992 , pp. 774 - 783
Copyright
Copyright © Canadian Mathematical Society 1992

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