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Title: Proving the characterization of Archimedean copulas via Dini derivatives (English)
Author: Fernández-Sánchez, Juan
Author: Úbeda-Flores, Manuel
Language: English
Journal: Kybernetika
ISSN: 0023-5954 (print)
ISSN: 1805-949X (online)
Volume: 52
Issue: 5
Year: 2016
Pages: 785-790
Summary lang: English
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Category: math
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Summary: In this note we prove the characterization of the class of Archimedean copulas by using Dini derivatives. (English)
Keyword: Archimedean copula
Keyword: derived number
Keyword: Dini derivative
MSC: 60E05
MSC: 62E10
idZBL: Zbl 06674939
idMR: MR3602015
DOI: 10.14736/kyb-2016-5-0785
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Date available: 2017-01-02T13:30:29Z
Last updated: 2018-01-10
Stable URL: http://hdl.handle.net/10338.dmlcz/145968
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Reference: [1] Alsina, C., Frank, M. J., Schweizer, B.: Associative Functions: Triangular Norms and Copulas..World Scientific, Singapore 2006. Zbl 1100.39023, MR 2222258, 10.1142/9789812774200
Reference: [2] Amo, E. de, Carrillo, M. Díaz, Sánchez, J. Fernández: Characterization of all copulas associated with non-continuous random variables..Fuzzy Sets Syst. 191 (2012), 103-112. MR 2874826, 10.1016/j.fss.2011.10.005
Reference: [3] Berg, L., Krüppel, M.: De Rahm's singular function and related functions..Z. Anal. Anw. 19 (2000), 227-237. MR 1748045, 10.4171/zaa/947
Reference: [4] Cherubini, U., Luciano, E., Vecchiato, W.: Copula Methods in Finance..Wiley Finance Series, John Wiley and Sons Ltd., Chichester 2004. Zbl 1163.62081, MR 2250804, 10.1002/9781118673331
Reference: [5] Durante, F., Jaworski, P.: A new characterization of bivariate copulas..Comm. Statist. Theory Methods 39 (2010), 2901-2912. Zbl 1203.62101, MR 2755533, 10.1080/03610920903151459
Reference: [6] Durante, F., Sempi, C.: Principles of Copula Theory..Chapman and Hall/CRC, London 2015. MR 3443023, 10.1201/b18674
Reference: [7] Genest, C., MacKay, J.: Copules archimédiennes et familles de lois bidimensionnelles dont les marges sont données..Canad. J. Statist. 14 (1986), 145-159. Zbl 0605.62049, MR 0849869, 10.2307/3314660
Reference: [8] Hagood, J. W., Thomson, B. S.: Recovering a function from a Dini derivative..Amer. Math. Monthly 113 (2006), 34-46. Zbl 1132.26321, MR 2202919, 10.2307/27641835
Reference: [9] Jaworski, P., Durante, F., Härdle, W., (editors), T. Rychlik: Copula Theory and its Applications..Lecture Notes in Statistics-Proceedings, Springer, Berlin-Heidelberg 2010. MR 3075361, 10.1007/978-3-642-12465-5
Reference: [10] Ling, C. H.: Representation of associative functions..Publ. Math. Debrecen 12 (1965), 189-212. Zbl 0137.26401, MR 0190575
Reference: [11] Łojasiewicz, S.: An Introduction to the Theory of Real Functions. Third Edition..A Wiley-Interscience Publication, John Wiley and Sons Ltd., Chichester 1988. MR 0952856
Reference: [12] McNeil, A. J., Nešlehová, J.: Multivariate Archimedean copulas, $d$-monotone functions and $l_1$-norm symmetric distributions..Ann. Stat. 37 (2009), 3059-3097. MR 2541455, 10.1214/07-aos556
Reference: [13] McNeil, A. J., Frey, R., Embrechts, P.: Quantitative Risk Management: Concepts, Techniques, and Tools..Princeton University Press, Princeton 2005. Zbl 1347.00025, MR 2175089
Reference: [14] Natanson, L. P.: Theory of Functions of a Real Variable. Vol. I, revised edition..Frederick Ungar Publishing, New York 1961. MR 0148805
Reference: [15] Nelsen, R. B.: An Introduction to Copulas. Second Edition..Springer, New York 2006. MR 2197664, 10.1007/0-387-28678-0
Reference: [16] Schweizer, B., Sklar, A.: Probabilistic Metric Spaces..North-Holland, New York 1983. Reprinted, Dover, Mineola NY, 2005. Zbl 0546.60010, MR 0790314
Reference: [17] Sklar, A.: Fonctions de répartition à n dimensions et leurs marges..Publ. Inst. Statist. Univ. Paris 8 (1959), 229-231. MR 0125600
Reference: [18] Wysocki, W.: Characterizations of Archimedean n-copulas..Kybernetika 51 (2015), 212-230. Zbl 1340.62054, MR 3350557, 10.14736/kyb-2015-2-0212
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