Semi-copulas, capacities and families of level sets

Fuzzy Sets and Systems

Volumn 161, Issue 2, 2010, Pages 269-276

  Durante, Fabrizio ^a   Spizzichino, Fabio ^b  

^a JOHANNES KEPLER UNIVERSITY LINZ   (Austria)

^b SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

Bivariate ageing function; Capacity; Copula; Non additive measure; Semi copula; Survival models

Indexed keywords

BIVARIATE; BIVARIATE AGEING FUNCTION; NON-ADDITIVE MEASURE; SEMI-COPULA; SURVIVAL MODEL;

LEVEL MEASUREMENT;

MEASUREMENTS;

EID: 70449700571     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.fss.2009.03.002     Document Type: Article

References (41)

1. Alvoni E., Papini P.L., and Spizzichino F. On a class of transformations of copulas and quasi-copulas. Fuzzy Sets and Systems 160 3 (2009) 334-343
2. Arnold B.C., Castillo E., and Sarabia J.M. Multivariate distributions defined in terms of contours. J. Statist. Plann. Inference 138 12 (2008) 4158-4171
3. Barlow R.E., and Mendel M.B. de Finetti-type representations for life distributions. J. Amer. Statist. Assoc. 87 420 (1992) 1116-1122
4. Barlow R.E., and Spizzichino F. Schur-concave survival functions and survival analysis. J. Comput. Appl. Math. 46 3 (1993) 437-447
5. B. Bassan, F. Spizzichino, Dependence and multivariate aging: the role of level sets of the survival function, in: System and Bayesian Reliability, Series of Quality Reliability Engineering Statistics, Vol. 5, World Scientific Publishers, River Edge, NJ, 2001, pp. 229-242.
6. B. Bassan, F. Spizzichino, On some properties of dependence and aging for residual lifetimes in the exchangeable case, in: Mathematical and Statistical Methods in Reliability, Series of Quality Reliability Engineering Statistics, Trondheim, 2002, Vol. 7, World Scientific Publisher, River Edge, NJ, 2003, pp. 235-249.
7. Bassan B., and Spizzichino F. Bivariate survival models with Clayton aging functions. Insurance Math. Econom. 37 1 (2005) 6-12
8. Bassan B., and Spizzichino F. Relations among univariate aging, bivariate aging and dependence for exchangeable lifetimes. J. Multivariate Anal. 93 2 (2005) 313-339
9. Burchard A., and Hajaiej H. Rearrangement inequalities for functionals with monotone integrands. J. Funct. Anal. 233 2 (2006) 561-582
10. Capéraà P., Fougères A.-L., and Genest C. Bivariate distributions with given extreme value attractor. J. Multivariate Anal. 72 1 (2000) 30-49
11. Choquet G. Theory of capacities. Ann. Inst. Fourier Grenoble 5 (1955) 131-295 1953-1954
12. De Baets B., Janssens S., and De Meyer H. Meta-theorems on inequalities for scalar fuzzy set cardinalities. Fuzzy Sets and Systems 157 11 (2006) 1463-1476
13. de Finetti B. Sulle stratificazioni convesse. Ann. Mat. Pura Appl. (4) 30 (1949) 173-183
14. Denneberg D. Non-additive Measure and Integral (1994), Kluwer Academic Publishers, Dordrecht
15. D. Denneberg, Non-additive measure and integral, basic concepts and their role for applications, in: Fuzzy Measures and Integrals, Studies in Fuzziness and Soft Computing, Vol. 40, Physica, Heidelberg, 2000, pp. 42-69.
16. F. Durante, R. Foschi, P. Sarkoci, Distorted copulas: constructions and tail dependence, 2008, submitted for publication.
17. F. Durante, R. Ghiselli Ricci, Supermigrative semi-copulas and triangular norms, Inform. Sci. (2009), in press.
18. Durante F., Klement E.P., Mesiar R., and Sempi C. Conjunctors and their residual implicators: characterizations and construction methods. Mediterr. J. Math. 4 3 (2007) 343-356
19. Durante F., Quesada-Molina J.J., and Sempi C. Semicopulas: characterizations and applicability. Kybernetika (Prague) 42 3 (2006) 287-302
20. Durante F., and Sempi C. Copula and semicopula transforms. Internat. J. Math. Math. Sci. 2005 4 (2005) 645-655
21. Durante F., and Sempi C. Semicopulæ. Kybernetika (Prague) 41 3 (2005) 315-328
22. Foschi R., and Spizzichino F. Semigroups of semicopulas and evolution of dependence at increase of age. Mathware Soft Comput. XV 1 (2008) 95-111
23. Genest C., and Rivest L.-P. On the multivariate probability integral transformation. Statist. Probab. Lett. 53 4 (2001) 391-399
24. Ghirardato P. On independence for non-additive measures, with a Fubini theorem. J. Econom. Theory 73 2 (1997) 261-291
25. Guerraggio A., and Molho E. The origins of quasi-concavity: a development between mathematics and economics. Historia Math. 31 1 (2004) 62-75
26. Hajek P., and Mesiar R. On copulas, quasicopulas and fuzzy logic. Soft Comput. 12 12 (2008) 1239-1243
27. H. Joe, Multivariate Models and Dependence Concepts, Monographs on Statistics and Applied Probability, Vol. 73, Chapman & Hall, London, 1997.
28. E.P. Klement, R. Mesiar, E. Pap, Triangular Norms, Trends in Logic. Studia Logica Library, Vol. 8, Kluwer Academic Publishers, Dordrecht, 2000.
29. Klement E.P., Mesiar R., and Pap E. Archimax copulas and invariance under transformations. C. R. Math. Acad. Sci. Paris 340 (2005) 755-758
30. E.P. Klement, R. Mesiar, and E. Pap, A universal integral as common frame for Choquet and Sugeno Integral, 2009, submitted for publication.
31. Morillas P.M. A characterization of absolutely monotonic (Δ) functions of a fixed order. Publ. Inst. Math. (Beograd) (N.S.) 78 92 (2005) 93-105
32. Morillas P.M. A method to obtain new copulas from a given one. Metrika 61 2 (2005) 169-184
33. G. Nappo, F. Spizzichino, Relations between the Kendall distribution and the family of the level sets of a bivariate survival models, Inform. Sci. (2009), in press.
34. R.B. Nelsen, An Introduction to Copulas, second ed., Springer Series in Statistics, Springer, New York, 2006.
35. E. Pap (Ed.), Handbook of Measure Theory, Vols. I, II, North-Holland, Amsterdam, 2002.
36. Saminger-Platz S., and Sempi C. A primer on triangle functions I. Aequationes Math. 76 3 (2008) 1-40
37. M. Scarsini, Copulae of capacities on product spaces, in: Distributions with Fixed Marginals and Related Topics, Seattle, WA, 1993, IMS Lecture Notes in Monograph Series, Vol. 28, Institute Mathematical Statistics, Hayward, CA, 1996, pp. 307-318.
38. Sklar A. Fonctions de répartition à n dimensions et leurs marges. Publ. Inst. Statist. Univ. Paris 8 (1959) 229-231
39. F. Spizzichino, Subjective Probability Models for Lifetimes, Monographs on Statistics and Applied Probability, Vol. 91, Chapman & Hall, CRC, Boca Raton, FL, 2001.
40. Spizzichino F. A concept of duality for multivariate exchangeable survival models. Fuzzy Sets and Systems 160 3 (2009) 325-333
41. Suárez-García F., and Gil-Álvarez P. Two families of fuzzy integrals. Fuzzy Sets and Systems 18 (1986) 67-81