Threshold copulas and positive dependence

Fabrizio Durante, Rachele Foschi and Fabio Spizzichino

Statistics & Probability Letters, 2008, vol. 78, issue 17, 2902-2909

Abstract: Starting with a notion of positive dependence and with the family of the lower threshold copulas Ct associated with a bivariate distribution having copula C, we define different notions of positive dependence for C, reflecting the dependence properties of the copulas Ct for some t. Then, we analyze some structural aspects of lower threshold copulas and of the given definitions. Furthermore we consider several specific cases arising from relevant special choices of (e.g., PQD, LTD, TP2 and PLR). Our analysis, in particular, allows us to present a number of relevant examples and counter-examples, which can be useful in the study of the tail dependence for a bivariate distribution.

Date: 2008
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