Some positive dependence stochastic orders. (English) Zbl 1086.62009
Some stochastic orders of positive dependence that arise when the underlying random vectors are ordered with respect to some multivariate hazard rate stochastic orders, and have the same univariate marginal distributions, are studied. It is shown how the orders can be studied by restricting them to copulae, and a number of examples is given. Some positive dependence concepts that arise from the new positive dependence orders are discussed. The relationship of the new orders to other positive dependence orders that have appeared in the literature is established.
Reviewer: Jaroslaw Bartoszewicz (Wrocław)
MSC:
| 62E10 | Characterization and structure theory of statistical distributions |
| 60E15 | Inequalities; stochastic orderings |
| 62N05 | Reliability and life testing |
| 62H05 | Characterization and structure theory for multivariate probability distributions; copulas |
Keywords:
Copula; Fréchet classes and bounds; Marshal-Olkin distributions; Left tail decreasing; Right tail increasing; Multivariate total positivity; Likelihood ratio order; Lower orthant decreasing ratio order; Upper orthant increasing ratio orderReferences:
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