| 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.
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. |
