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Some concepts of positive dependence for bivariate interchangeable distributions

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Abstract

In this work we consider some familiar and some new concepts of positive dependence for interchangeable bivariate distributions. By characterizing distributions which are positively dependent according to some of these concepts, we indicate real situations in which these concepts arise naturally. For the various families of positively dependent distributions we prove some closure properties and demonstrate all the possible logical relations. Some inequalities are shown and applied to determine whether under- (or over-) estimates, of various probabilistic quantities, occur when a positively dependent distribution is assumed (falsely) to be the product of its marginals (that is, when two positively dependent random variables are assumed, falsely, to be independent). Specific applications in reliability theory, statistical mechanics and reversible Markov processes are discussed.

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Authors and Affiliations

  1. University of New Mexico, New Mexico, USA

    Moshe Shaked

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  1. Moshe Shaked
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Additional information

This work was partially supported by National Science Foundation GP-30707X1. It is part of the author's Ph.D. dissertation prepared at the University of Rochester and supervised by A. W. Marshall.

Now at Indiana University.

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Shaked, M. Some concepts of positive dependence for bivariate interchangeable distributions. Ann Inst Stat Math 31, 67–84 (1979). https://doi.org/10.1007/BF02480266

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  • DOI: https://doi.org/10.1007/BF02480266

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