Copula and semicopula transforms

International Journal of Mathematics and Mathematical Sciences

Volumn 2005, Issue 4, 2005, Pages 645-655

  Durante, Fabrizio ^a   Sempi, Carlo ^a  

^a UNIVERSITY OF SALENTO   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 24944525658     PISSN: 01611712     EISSN: None     Source Type: Journal    
DOI: 10.1155/IJMMS.2005.645     Document Type: Article

References (28)

1. C. Alsina, R. B. Nelsen, and B. Schweizer, On the characterization of a class of binary operations on distribution functions, Statist. Probab. Lett. 17 (1993), no. 2, 85-89.
2. R. E. Barlow and F. Spizzichino, Schur-concave survival functions and survival analysis, J. Comput. Appl. Math. 46 (1993), no. 3, 437-447.
3. B. Bassan and F. Spizzichino, Relations among univariate aging, bivariate aging and dependence for exchangeable lifetimes, J. Multivariate Anal. 93 (2005), no. 2, 313-339.
4. T. Calvo, A. Kolesárová, M. Komorníková, and R. Mesiar, Aggregation operators: properties, classes and construction methods, Aggregation Operators. New Trends and Applications (T. Calvo, R. Mesiar, and G. Mayor, eds.), Stud. Fuzziness Soft Comput., vol. 97, Physica, Heidelberg, 2002, pp. 3-104.
5. P. Capéraà, A.-L. Fougères, and C. Genest, Bivariate distributions with given extreme value attractor, J. Multivariate Anal. 72 (2000), no. 1, 30-49.
6. I. Cuculescu and R. Theodorescu, Extreme value attractors for star unimodal copulas, C. R. Math. Acad. Sci. Paris 334 (2002), no. 8, 689-692.
7. D. Denneberg, Non-additive Measure and Integral, Theory and Decision Library. Series B: Mathematical and Statistical Methods, vol. 27, Kluwer Academic Publishers, Dordrecht, 1994.
8. F. Durante and C. Sempi, Semicopulæ, to appear in Kybernetika.
9. F. Durante and C. Sempi, Compositions of copulas and quasi-copulas, Soft Methodology and Random Information Systems (M. López-Díaz, M. Á. Gil, P. Grzegorzewski, O. Hryniewicz, and J. Lawry, eds.), Advances in Soft Computing, Springer, Berlin, 2004, pp. 189-196.
10. E. W. Frees and E. A. Valdez, Understanding relationships using copulas, N. Am. Actuar. J. 2 (1998), no. 1, 1-25.
11. C. Genest and R. J. MacKay, Copules archimédiennes et familles de lois bidimensionnelles dont les marges sont données [Archimedean copulas and families of two-dimensional distributions with fixed marginals], Canad. J. Statist. 14 (1986), no. 2, 145-159 (French).
12. C. Genest, J. J. Quesada Molina, J. A. Rodríguez Lallena, and C. Sempi, A characterization of quasi-copulas, J. Multivariate Anal. 69 (1999), no. 2, 193-205.
13. C. Genest and L.-P. Rivest, On the multivariate probability integral transformation, Statist. Probab. Lett. 53 (2001), no. 4, 391-399.
14. S. Janssens, B. De Baets, and H. De Meyer, Bell-type inequalities for quasi-copulas, Fuzzy Sets and Systems 148 (2004). no. 2. 263-278.
15. E. P. Klement, R. Mesiar, and E. Pap, Triangular Norms, Trends in Logic-Studia Logica Library, vol. 8, Kluwer Academic Publishers, Dordrecht, 2000.
16. E. P. Klement, R. Mesier, and E. Pap, Transformations of copulas and quasi-copulas, Soft Methodology and Random Information Systems (M. López-Díaz, M. Á. Gil, P. Grzegorzewski, O. Hryniewicz, and J. Lawry, eds.), Advances in Soft Computing, Springer, Berlin, 2004, pp. 181-188.
17. A. W. Marshall and I. Olkin, Inequalities: Theory of Majorization and Its Applications, Mathematics in Science and Engineering, vol. 143, Academic Press, New York, 1979.
18. A. W. Marshall and I. Olkin, Domains of attraction of multivariate extreme value distributions, Ann. Probab. 11 (1983), no. 1, 168-177.
19. R. B. Nelsen, An Introduction to Copulas, Lecture Notes in Statistics, vol. 139, Springer-Verlag, New York, 1999.
20. R. B. Nelsen, J. J. Quesada-Molina, B. Schweizer, and C. Sempi, Derivability of some operations on distribution functions, Distributions with Fixed Marginals and Related Topics (Seattle, WA, 1993) (L. Rüschendorf, B. Schweizer, and M. D. Taylor, eds.), IMS Lecture Notes Monogr. Ser., vol. 28, Inst. Math. Statist., California, 1996, pp. 233-243.
21. R. B. Nelsen, J. J. Quesada-Molina, B. Schweizer, and C. Sempi, Some new properties of quasi-copulas, Distributions with Given Marginals and Statistical Modelling (C. M. Cuadras, J. Fortiana, and J. A. Rodríguez Lallena, eds.), Kluwer Academic Publishers, Dordrecht, 2002, pp. 187-194.
22. B. Schweizer and A. Sklar, Probabilistic Metric Spaces, North-Holland Series in Probability and Applied Mathematics, North-Holland Publishing, New York, 1983.
23. C. Sempi, Copulæ and their uses, Mathematical and Statistical Methods in Reliability (Trondheim, 2002) (B. H. Lindqvist and K. A. Doksum, eds.), Ser. Qual. Reliab. Eng. Stat., vol. 7, World Scientific Publishing, New Jersey, 2003, pp. 73-85.
24. M. Sklar, Fonctions de répartition à n dimensions et leurs marges, Publ. Inst. Statist. Univ. Paris 8 (1959), 229-231 (French).
25. F. Spizzichino, Subjective Probability Models for Lifetimes, Monographs on Statistics and Applied Probability, vol. 91, Chapman & Hall/CRC, Florida, 2001.
26. F. Suárez García and P. Gil Álvarez, Two families of fuzzy integrals, Fuzzy Sets and Systems 18 (1986). no. 1, 67-81.
27. M. Úbeda Flores, Cópulas y quasicópulas: interrelaciones y nuevas propiedades. Aplicaciones, Ph.D. Dissertation, Universidad de Almería, Servicio de Publicaciones de la Universidad de Almería, Spain, 2001.
28. S. S. Wang, V. R. Young, and H. H. Panjer, Axiomatic characterization of insurance prices, Insurance Math. Econom. 21 (1997). no. 2. 173-183.