Some positive dependence stochastic orders

Marco Scarsini (1, 2) , Antonio Colangelo , Moshe Shaked

1 GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC
2 Dipartimento di Scienze Economiche e Aziendali

In this paper we study 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. We show how the orders can be studied by restricting them to copulae, we give a number of examples, and we study some positive dependence concepts that arise from the new positive dependence orders. We also discuss the relationship of the new orders to other positive dependence orders that have appeared in the literature.

Keywords: Copula; Fréchet classes and bounds; Marshall–Olkin distributions; Farlie–Gumbel–Morgenstern distributions; Archimedean copula; Left tail decreasing (LTD); Right tail increasing (RTI); Multivariate total positivity; Likelihood ratio order; Lower orthant decreasing ratio (lodr) order; Upper orthant increasing ratio (uoir) order

Domains: Economy and decision science

Marco Scarsini, Antonio Colangelo, Moshe Shaked. Some positive dependence stochastic orders. Journal of Multivariate Analysis, 2006, Vol.97, N°1, pp. 46-78. ⟨10.1016/j.jmva.2004.11.006⟩. ⟨hal-00539122⟩