Article
Full entry |
PDF
(0.3 MB)
Feedback
PDF
(0.3 MB)
Feedback
Keywords:
copulas; semi-copulas; evolution of ageing and dependence; action of a semigroup
copulas; semi-copulas; evolution of ageing and dependence; action of a semigroup
Summary:
In previous papers, evolution of dependence and ageing, for vectors of non-negative random variables, have been separately considered. Some analogies between the two evolutions emerge however in those studies. In the present paper, we propose a unified approach, based on semigroup arguments, explaining the origin of such analogies and relations among properties of stochastic dependence and ageing.
References:
[1] Bassan, B., Spizzichino, F.: Dependence and multivariate aging: the role of level sets of the survival function. In: System and Bayesian Reliability, Series on Quality, Reliability and Engineering Statistics, vol. 5, World Scientific Publishing, River Edge, NJ 2001, pp. 229-242. DOI 10.1142/9789812799548_0013 | MR 1896784
[2] Bassan, B., Spizzichino, F.: On some properties of dependence and aging for residual lifetimes in the exchangeable case. In: Mathematical and Statistical Methods in Reliability (Trondheim, 2002), Series on Quality, Reliability and Engineering Statistics, vol. 7, World Scientific Publishing, River Edge, NJ 2003, pp. 235-249. MR 2031077
[3] Bassan, B., Spizzichino, F.: Relations among univariate aging, bivariate aging and dependence for exchangeable lifetimes. J. Multivariate Anal. 93 (2005), 2, 313-339. DOI 10.1016/j.jmva.2004.04.002 | MR 2162641 | Zbl 1070.60015
[4] Durante, F., Foschi, R., Sarkoci, P.: Distorted copulas: constructions and tail dependence. Comm. Statist. 39 (2010), 2288-2301. DOI 10.1080/03610920903039506 | MR 2755652 | Zbl 1194.62075
[5] Durante, F., Foschi, R., Spizzichino, F.: Threshold copulas and dependence properties. Statist. Probab. Lett. 78 (2008), 2902-2909. DOI 10.1016/j.spl.2008.04.013 | MR 2474379
[6] Durante, F., Foschi, R., Spizzichino, F.: Ageing functions and multivariate notions of NBU and IFR. Probab. Engrg. Inform. Sci. 24 (2010), 2, 263-278. DOI 10.1017/S026996480999026X | MR 2602143
[7] Durante, F., Ricci, R. Ghiselli: Supermigrative copulas and positive dependence. Adv. in Statist. Anal. 96 (2012), 327-342. DOI 10.1007/s10182-011-0165-2 | MR 2956371
[8] Durante, F., Quesada-Molina, J., Sempi, C.: Semicopulas: characterizations and applicability. Kybernetika 42 (2006), 3, 287-302. MR 2253390 | Zbl 1249.60016
[9] Durante, F., Sempi, C.: Copula and semicopula transforms. Internat. J. Math. and Math. Sci. 4 (2005), 645-655. DOI 10.1155/IJMMS.2005.645 | MR 2172400 | Zbl 1078.62055
[10] Durante, F., Sempi, C.: Semicopulae. Kybernetika 41 (2005), 3, 315-328. MR 2181421 | Zbl 1249.26021
[11] Foschi, R.: Evolution of Conditional Dependence of Residual Lifetimes. Ph.D. Thesis, Università degli Studi di Roma La Sapienza - Dipartimento di Matematica G. Castelnuovo, 2010.
[12] Foschi, R., Spizzichino, F.: Semigroups of semicopulas and evolution of dependence at increase of age. Mathware and Soft Computing XV (2008), 1, 95-111. MR 2459040
[13] Jacobson, N.: Basic Algebra. I. W. H. Freeman and Company, New York 1985. MR 0780184 | Zbl 0557.16001
[14] Joe, H.: Multivariate Models and Dependence Concepts. Chapman and Hall, London 1997. MR 1462613 | Zbl 0990.62517
[15] Joe, H.: An Introduction to Copulas. Second edition. Springer Series in Statistics, Springer, New York 2006. MR 2197664
Search
Partner of
