The analytical expression for the degree of multivariate discordance in probability has a high level of mathematical elegance. This is why we were interested in the degree of discrepancy. In addition, while working on this expression, an application to the Bernstein copula appeared more accessible. We therefore modeled the expression for the Bernstein copula and the degree of discordance.

copulas, multivariate dependence, degree of discordance, logistics model

Received: May 3, 2024; Revised: June 7, 2024; Accepted: June 24, 2024; Published: October 19, 2024

How to cite this article: Vini Yves Bernadin LOYARA, Fabrice OUOBA and Remi Guillaume BAGRE, Copula of Bernstein and degree of discordance, Far East Journal of Theoretical Statistics 68(3) (2024), 385-404. https://doi.org/10.17654/0972086324021

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

References:
[1] B. Diakarya, Sampling a survival and conditional class of Archimedean processes, Journal of Mathematics Research 5(1) (2013). doi:10.5539/jmr.v5n1p53.
[2] A. Charpentier and J. Segers, Tails of multivariate Archimedean copulas, J. Multivariate Anal. 100 (2009), 1521-1537. doi:10.1016/j.jmva.2008.12.015.
[3] H. Joe, Multivariate models and dependence concepts monographs on statistics and applied probability, 73, Chapman and Hall, London, 1997.
[4] Korotimi Ouédraogo and Diakarya Barro, An approach of estimating the value at risk of heavy-tailed distribution using copulas, European Journal of Pure and Applied Mathematics 15(4) (2022), 2074-2085. ejpam.com Published by New York Business Global.
[5] R. B. Nelsen, An Introduction to Copulas, Lectures Notes in Statistics 139, Springer-Verlag, 1999.
[6] H. Noh, A. E. Ghouch and Keilegom, Semiparametric conditional quantile estimation through copula-based multivariate models, Journal of Business and Economic Statistics (2013). DOI:10.1080/07350015.2014.926171.
[7] A. J. Patton, Modelling Time-varying Exchange Rate Dependence using the Conditional Copula, Ph. D. Thesis, Department of Economics, UCSD, 2001.
[8] B. Remillard, B. Nasri and Bouezmarni, On copula-based conditional quantile estimators, Statistics and Probability Letters, Statistics and Probability Letters Volume 128 (2017), 14-20. http://dx.doi.org/10.1016/j.spl.2017.04.014.
[9] R. T. Rockafeller, Coherent approaches to risk in optimization under uncertainty, Tutorials in Operations Research INFORMS (2007), 38-61.
[10] H. Rootzén and C. Klüppelberg, A Single Number Can’t Hedge Against Economic Catastrophes, Working Paper, Munich University of Technology, 1999.
[11] A. Sklar, Random variables, distribution functions, and copulas a personal look backward and forward, Distributions with Fixed Marginals and Related Topics, 28 (1996), 1-14.
[12] S. Dossou-Gbete, B. Some and D. Barro, Modelling the dependence of parametric bivariate extreme value copulas, Asian Journal of Mathematics and Statistics 2(3) (2009), 41-54. DOI:10.3923/ajms.2009.41.54.
URL: http://scialert.net/abstract/?doi=ajms.2009.41.54.
[13] Yves Bernadin Vini Loyara, Remi Guillaume Bagré and Diakarya Barro, Multivariate risks modeling for financial portfolio management and climate applications, Far East Journal of Math. Sci. (FJMS) (2018).
[14] Yves Bernadin Vini Loyara and Diakarya Barro, Value-at-risk modeling with conditional copulas in euclidean space framework, European Journal of Pure and Applied Mathematics (EJPAM) (2019).