Hyper-dependence, hyper-ageing properties and analogies between them: a semigroup-based approach

Rachele Foschi

Kybernetika (2013)

  • Volume: 49, Issue: 1, page 96-113
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Foschi, Rachele. "Hyper-dependence, hyper-ageing properties and analogies between them: a semigroup-based approach." Kybernetika 49.1 (2013): 96-113. <http://eudml.org/doc/252549>.

@article{Foschi2013,
abstract = {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.},
author = {Foschi, Rachele},
journal = {Kybernetika},
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},
language = {eng},
number = {1},
pages = {96-113},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Hyper-dependence, hyper-ageing properties and analogies between them: a semigroup-based approach},
url = {http://eudml.org/doc/252549},
volume = {49},
year = {2013},
}

TY - JOUR
AU - Foschi, Rachele
TI - Hyper-dependence, hyper-ageing properties and analogies between them: a semigroup-based approach
JO - Kybernetika
PY - 2013
PB - Institute of Information Theory and Automation AS CR
VL - 49
IS - 1
SP - 96
EP - 113
AB - 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.
LA - eng
KW - copulas; semi-copulas; evolution of ageing and dependence; action of a semigroup; copulas; semi-copulas; evolution of ageing and dependence; action of a semigroup
UR - http://eudml.org/doc/252549
ER -

References

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  1. Bassan, B., Spizzichino, F., 10.1142/9789812799548_0013, In: System and Bayesian Reliability, Series on Quality, Reliability and Engineering Statistics, vol. 5, World Scientific Publishing, River Edge, NJ 2001, pp. 229-242. MR1896784DOI10.1142/9789812799548_0013
  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. MR2031077
  3. Bassan, B., Spizzichino, F., 10.1016/j.jmva.2004.04.002, J. Multivariate Anal. 93 (2005), 2, 313-339. Zbl1070.60015MR2162641DOI10.1016/j.jmva.2004.04.002
  4. Durante, F., Foschi, R., Sarkoci, P., 10.1080/03610920903039506, Comm. Statist. 39 (2010), 2288-2301. Zbl1194.62075MR2755652DOI10.1080/03610920903039506
  5. Durante, F., Foschi, R., Spizzichino, F., 10.1016/j.spl.2008.04.013, Statist. Probab. Lett. 78 (2008), 2902-2909. MR2474379DOI10.1016/j.spl.2008.04.013
  6. Durante, F., Foschi, R., Spizzichino, F., 10.1017/S026996480999026X, Probab. Engrg. Inform. Sci. 24 (2010), 2, 263-278. MR2602143DOI10.1017/S026996480999026X
  7. Durante, F., Ricci, R. Ghiselli, 10.1007/s10182-011-0165-2, Adv. in Statist. Anal. 96 (2012), 327-342. MR2956371DOI10.1007/s10182-011-0165-2
  8. Durante, F., Quesada-Molina, J., Sempi, C., Semicopulas: characterizations and applicability., Kybernetika 42 (2006), 3, 287-302. Zbl1249.60016MR2253390
  9. Durante, F., Sempi, C., 10.1155/IJMMS.2005.645, Internat. J. Math. and Math. Sci. 4 (2005), 645-655. Zbl1078.62055MR2172400DOI10.1155/IJMMS.2005.645
  10. Durante, F., Sempi, C., Semicopulae., Kybernetika 41 (2005), 3, 315-328. Zbl1249.26021MR2181421
  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. MR2459040
  13. Jacobson, N., Basic Algebra. I., W. H. Freeman and Company, New York 1985. Zbl0557.16001MR0780184
  14. Joe, H., Multivariate Models and Dependence Concepts., Chapman and Hall, London 1997. Zbl0990.62517MR1462613
  15. Joe, H., An Introduction to Copulas. Second edition., Springer Series in Statistics, Springer, New York 2006. MR2197664

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