Title:
|
Semicopulæ (English) |
Author:
|
Durante, Fabrizio |
Author:
|
Sempi, Carlo |
Language:
|
English |
Journal:
|
Kybernetika |
ISSN:
|
0023-5954 |
Volume:
|
41 |
Issue:
|
3 |
Year:
|
2005 |
Pages:
|
[315]-328 |
Summary lang:
|
English |
. |
Category:
|
math |
. |
Summary:
|
We define the notion of semicopula, a concept that has already appeared in the statistical literature and study the properties of semicopulas and the connexion of this notion with those of copula, quasi-copula, $t$-norm. (English) |
Keyword:
|
semicopula |
Keyword:
|
copula |
Keyword:
|
quasi-copula |
Keyword:
|
aggregation operator |
Keyword:
|
$t$-norm |
MSC:
|
26B35 |
MSC:
|
60E05 |
idZBL:
|
Zbl 1249.26021 |
idMR:
|
MR2181421 |
. |
Date available:
|
2009-09-24T20:09:08Z |
Last updated:
|
2015-03-23 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135658 |
. |
Reference:
|
[1] Agell N.: On the concavity of t-norms and triangular functions.Stochastica 8 (1984), 91–95 Zbl 0567.26010, MR 0780142 |
Reference:
|
[2] Alsina C., Nelsen R. B., Schweizer B.: On the characterization of a class of binary operations on distribution functions.Statist. Probab. Lett. 17 (1993), 85–89 Zbl 0798.60023, MR 1223530, 10.1016/0167-7152(93)90001-Y |
Reference:
|
[3] Bassan B., Spizzichino F.: Relations among univariate aging, bivariate aging and dependence for exchangeable lifetimes.J. Multivariate Anal. 93 (2005), 313–339 Zbl 1070.60015, MR 2162641, 10.1016/j.jmva.2004.04.002 |
Reference:
|
[4] Calvo T., Kolesárová A., Komorníková, M., Mesiar R.: Aggregation operators: properties, classes and construction methods.In: Aggregation Operators. New Trends and Applications (T. Calvo, R. Mesiar, and G. Mayor, eds.), Physica–Verlag, Heidelberg 2002, pp. 3–106 Zbl 1039.03015, MR 1936383 |
Reference:
|
[5] Calvo T., Mesiar R.: Stability of aggregation operators.In: Proc. EUSFLAT 2001, Leicester 2001, pp. 475–478 MR 1821982 |
Reference:
|
[6] Calvo T., Pradera A.: Double aggregation operators.Fuzzy Sets and Systems 142 (2004), 15–33 Zbl 1081.68105, MR 2045340, 10.1016/j.fss.2003.10.029 |
Reference:
|
[7] Dunford N., Schwartz J. T.: Linear Operators.Part I: General Theory. Wiley, New York 1958 Zbl 0635.47003, MR 1009162 |
Reference:
|
[8] Durante F., Sempi C.: On the characterization of a class of binary operations on bivariate distribution functions.Submitted Zbl 1121.60010 |
Reference:
|
[9] Fredricks G. A., Nelsen R. B.: Copulas constructed from diagonal sections.In: Distributions With Given Marginals and Moment Problems (V. Beneš and J. Štěpán, eds.), Kluwer Academic Publishers, Dordrecht 1997, pp. 129–136 Zbl 0906.60022, MR 1614666 |
Reference:
|
[10] Fredricks G. A., Nelsen R. B.: The Bertino family of copulas.In: Distributions with given marginals and statistical problems (C. M. Cuadras, J. Fortiana, and J. A. Rodríguez Lallena, eds.), Kluwer Academic Publishers, Dordrecht 2002, pp. 81–91 Zbl 1135.62334, MR 2058982 |
Reference:
|
[11] Genest C., Molina J. J. Quesada, Lallena J. A. Rodríguez, Sempi C.: A characterization of quasi-copulas.J. Multivariate Anal. 69 (1999), 193–205 MR 1703371, 10.1006/jmva.1998.1809 |
Reference:
|
[12] Kelley J. L.: General Topology.Van Nostrand, New York 1955; reprinted by Springer, New York – Heidelberg – Berlin 1975 Zbl 0066.16604, MR 0070144 |
Reference:
|
[13] Klement E. P., Mesiar, R., Pap E.: Triangular Norms.Kluwer Academic Publishers, Dordrecht 2000 Zbl 1087.20041, MR 1790096 |
Reference:
|
[14] Kolesárová A.: $1$-Lipschitz aggregation operators and quasi-copulas.Kybernetika 39 (2003), 615–629 MR 2042344 |
Reference:
|
[15] Mikusiński P., Sherwood, H., Taylor M. D.: The Fréchet bounds revisited.Real Anal. Exchange 17 (1991), 759–764 MR 1171416 |
Reference:
|
[16] Nelsen R. B.: An Introduction to Copulas.(Lecture Notes in Statistics 139.) Springer–Verlag, New York 1999 Zbl 1152.62030, MR 1653203, 10.1007/978-1-4757-3076-0 |
Reference:
|
[17] Nelsen R. B., Fredricks G. A.: Diagonal copulas.In: Distributions With Given Marginals and Moment Problems (V. Beneš and J. Štěpán, eds.), Kluwer Academic Publishers, Dordrecht 1997, pp. 121–128 Zbl 0906.60021, MR 1614665 |
Reference:
|
[18] Nelsen R. B., Quesada-Molina J. J., Schweizer, B., Sempi C.: Derivability of some operations on distribution functions.In: Distributions With Fixed Marginals and Related Topics (L. Rüschendorf, B. Schweizer, and M. D. Taylor, eds.), (IMS Lecture Notes – Monogr. Ser. 28), Inst. Math. Statist., Hayward 1996, pp. 233–243 MR 1485535 |
Reference:
|
[19] Nelsen R. B., Flores M. Úbeda: The lattice-theoretic structure of sets of bivariate copulas and quasi-copulas.Submitted |
Reference:
|
[20] Schweizer B., Sklar A.: Probabilistic Metric Spaces.Elsevier, New York 1983 Zbl 0546.60010, MR 0790314 |
Reference:
|
[21] Sklar A.: Fonctions de répartition à $n$ dimensions et leurs marges.Publ. Inst. Statist. Univ. Paris 8 (1959), 229–231 MR 0125600 |
Reference:
|
[22] Sklar A.: Random variables, joint distribution functions and copulas.Kybernetika 9 (1973), 449–460 Zbl 0292.60036, MR 0345164 |
Reference:
|
[23] Suarez F., Gil P.: Two families of fuzzy integrals.Fuzzy Sets and Systems 18 (1986), 67–81 Zbl 0595.28011, MR 0825620, 10.1016/0165-0114(86)90028-X |
Reference:
|
[24] Szász G.: Introduction to Lattice Theory.Academic Press, New York 1963 Zbl 0126.03703, MR 0166118 |
Reference:
|
[25] Flores M. Úbeda: Cópulas y quasicópulas: interrelaciones y nuevas propiedades.Aplicaciones. Ph. D. Dissertation. Universidad de Almería, Servicio de Publicaciones de la Universidad de Almería 2002 |
. |