Starting with a notion of positive dependence P and with the family of the lower threshold copulas C-t associated with a bivariate distribution having copula C, we define different notions of positive dependence for C, reflecting the dependence properties of the copulas C-t 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 P (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. (C) 2008 Elsevier B.V. All rights reserved.
Threshold copulas and positive dependence / Fabrizio, Durante; Rachele, Foschi; Spizzichino, Fabio. - In: STATISTICS & PROBABILITY LETTERS. - ISSN 0167-7152. - STAMPA. - 78:17(2008), pp. 2902-2909. [10.1016/j.spl.2008.04.013]
Threshold copulas and positive dependence
SPIZZICHINO, Fabio
2008
Abstract
Starting with a notion of positive dependence P and with the family of the lower threshold copulas C-t associated with a bivariate distribution having copula C, we define different notions of positive dependence for C, reflecting the dependence properties of the copulas C-t 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 P (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. (C) 2008 Elsevier B.V. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
