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EXTENDING DARSOW’S OPERATOR: A NEW FRAMEWORK FOR BIVARIATE AND MULTIVARIATE COPULAS
Keywords:
asymmetric copula, symmetric copula, Darsow operator, max-stablesDOI:
https://doi.org/10.17654/0972086325008Abstract
The Darsow product operator typically produces symmetric copulas unless one or more of the base copulas are asymmetric, which limits its applicability in scenarios where the data exhibit asymmetry. In this paper, we introduce a novel extension of the Darsow å-product operator that allows for the generation of more flexible asymmetric copulas which can be max-stable from symmetric base copulas (max-stables). We also provide some examples, explore properties of this new operator, and discuss its multivariate generalization.
Received: January 16, 2025
Accepted: March 6, 2025
References
A. Alfonsi and D. Brigo, New families of copulas based on periodic functions, Journal Communications in Statistics-Theory and Methods 34 (2005), 1437-1447.
D. E. Bernardino and D. Rulliere, On an asymmetric extension of multivariate Archimedean copulas, hal-01147778, (2016). from:
http://hal.archives-ouvertes.fr/hal-01147778.
L. Christophe, Construction of multivariate copulas and the compatibility problem (2007). Available at SSRN: https://ssrn.com/abstract=956041 or https://dx.doi.org/10.2139/ssrn.956041
W. F. Darsow, B. Nguyen and E. T. Olsen, Copulas and Markov processes, Illinois J. Math. 36(4) (1992), 600-642.
F. Durante, Construction of non-exchangeable bivariate distribution functions, Statist Papers 50 (2009), 383-391.
E. T. Olsen, W. F. Darsow and B. Nguyen, Copulas and Markov Operator, Illinois Institute of Technology, 28 (1996), 244-259.
A. Khoudraji, Constructions a l’etude des couples et a la modelisation de valeurs extremes bivariees (Ph. D. Thesis), Universite Laval, Quebec, Canada, 1995.
D. Kim and J. M. Kim, Analysis of directional dependence using asymmetric copula-based regression models, Journal of Statistical Computation and Simulation 84 (2014), 1990-2010.
W. Lee, M. Kim and J. Y. Ahn, On structural properties of an asymmetric copula family and its statistical implication, Fuzzy Sets and Systems 393 (2020), 126 142. https://doi.org/10.1016/j.fss.2019.06.004
E. Liebscher, Construction of asymmetric multivariate copulas, Journal of Multivariate Analysis 99 (2008), 2234-2250.
R. Mesiar and V. Najjari, New families of symmetric/asymmetric copulas, Fuzzy Sets and Systems 252 (2014), 99-110.
R. B. Nelsen, An Introduction to Copulas, 2nd ed., Springer, New York, 2006.
R. B. Nelsen, Extremes of nonexchangeability, Statistical Papers 48 (2007), 329-336.
J. A. Rodriguez-Lallena and M. Ubeda-Flores, A new class of bivariate copulas, Statistics and Probability Letters 66 (2004), 315-325.
A. Slar, Random variables, joint distribution functions and copulas, Kybernetika 9 (1973), 449-460.
S. Wu, Construction of asymmetric copulas and its application in two-dimensional reliability modeling, European Journal of Operational Research 238 (2014), 476-485.
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