Research Article
Year 2022,
Volume: 51 Issue: 2, 618 - 631, 01.04.2022
Abstract
References
- [1] C. Amblard and S. Girard, Symmetry and dependence properties within a semiparametric family of bivariate copulas, J. Nonparametr. Stat. 14 (6), 715-727, 2002.
- [2] I. Bairamov and K. Bairamov, From the Huang-Kotz FGM distribution to Bakers bivariate distribution, J. Multivariate Anal. 113, 106-115, 2013.
- [3] J. Carnicero, M. Wiper and M. Ausin, Density estimation of circular data with Bernstein polynomials, Hacet. J. Math. Stat. 47 (2), 273-286, 2018.
- [4] R. Cerqueti, and L. Claudio, Non-exchangeable copulas and multivariate total positivity, Inform. Sci. 360, 163-169, 2016.
- [5] M. Duncan, Applied Geometry for Computer Graphics and CAD, Springer Verlag, 2005.
- [6] F. Durante, E.P. Klement, C. Sempi and M. Ubeda-Flores, Measures of non- exchangeability for bivariate random vectors, Statist. Papers, 51 (3), 687-699, 2010.
- [7] T. Emura, S. Matsui and V. Rondeau, Survival Analysis with Correlated Endpoints, Joint Frailty-Copula Models, JSS Research Series in Statistics, Springer, 2019.
- [8] W. Feller, An Introduction to Probability Theory and its Applications, Wiley, 1965.
- [9] Y. Jun, Enjoy the joy of copulas: with a package copula, J. Stat. Softw. 21 (4), 1-21, 2007.
- [10] R.B. Nelsen, An Introduction to Copulas, Springer, 2007.
- [11] R.B. Nelsen, Extremes of nonexchangeability, Statist. Papers, 48 (2), 329-336, 2007.
- [12] D. Pfeifer and O. Ragulina, Adaptive Bernstein copulas and risk management, Mathematics, 8 (12), 1-22, 2020.
- [13] J.A. Rodriguez Lallena, Estudio de la compatibilidad y diseño de nuevas familias en la teoría de cópulas aplicaciones, PhD thesis, Universidad de Granada, 1992.
- [14] S. Saekaow and S. Tasena, Sobolev convergence of empirical Bernstein copulas, Hacet. J. Math. Stat. 48 (6), 1845-1858, 2019.
- [15] A. Sklar, Fonctions de repartition a n dimensions et leurs marges, Publ. Inst. Stat. Univ. Paris 8, 229-231, 1959.
- [16] L.H. Sun, X.W. Huang, M.S. Alqawba, J.M. Kim and T. Emura, Copula-based Markov Models for Time Series-Parametric Inference and Process Control, JSS Research Series in Statistics, Springer, 2020.
- [17] S.O. Susam, Parameter estimation of some Archimedean copulas based on minimum Cramér-von-Mises distance, J. Iran. Stat. Soc. (JIRSS) 19 (1), 163-183, 2020.
- [18] S.O. Susam and M.S. Erdogan, Plug-in estimation of dependence characteristics of Archimedean copula via Bézier curve, REVSTAT, 1-17, In Press.
- [19] S.O. Susam and B.H. Ucer, Testing independence for Archimedean copula based on Bernstein estimate of Kendall distribution function, J. Stat. Comput. Simul. 88 (13), 2589-2599, 2018.
- [20] S.O. Susam and B.H. Ucer, A goodness-of-fit test based on Bézier curve estimation of Kendall distribution, J. Stat. Comput. Simul. 90 (7), 1194-1215, 2020.
- [21] S.O. Susam and B.H. Ucer, On construction of Bernstein-Bézier type bivariate Archimedean copula, REVSTAT, 1-17, In Press.
- [22] M. Úbeda Flores, Introducción a la teoria de cópulas. Aplicaciones, Predoctoral Research Dissertation, Universidad de Almeria, 1998.
- [23] G. Weiß, Parameter estimation by maximum-likelihood and minimum-distance estimators: a simulation study, Comput. Statist. 26 (1), 31-54, 2011.
A multi-parameter Generalized Farlie-Gumbel-Morgenstern bivariate copula family via Bernstein polynomial
Abstract
In this paper, we are proposing a flexible method for constructing a bivariate generalized Farlie-Gumbel-Morgenstern (G-FGM) copula family. The method is mainly developed around the function $\phi(t)$ ($t\in [0,1]$), where $\phi$ is the generator of the G-FGM copula. The proposed construction method has useful advantages. The first of which is the direct relationship between the $\phi$ function and Kendall's tau. The second advantage is the possibility of constructing a multi-parameter G-FGM copula which allows us to better harmonize empirical instruction with the model. The construction method is illustrated by three real data examples.
Keywords
References
- [1] C. Amblard and S. Girard, Symmetry and dependence properties within a semiparametric family of bivariate copulas, J. Nonparametr. Stat. 14 (6), 715-727, 2002.
- [2] I. Bairamov and K. Bairamov, From the Huang-Kotz FGM distribution to Bakers bivariate distribution, J. Multivariate Anal. 113, 106-115, 2013.
- [3] J. Carnicero, M. Wiper and M. Ausin, Density estimation of circular data with Bernstein polynomials, Hacet. J. Math. Stat. 47 (2), 273-286, 2018.
- [4] R. Cerqueti, and L. Claudio, Non-exchangeable copulas and multivariate total positivity, Inform. Sci. 360, 163-169, 2016.
- [5] M. Duncan, Applied Geometry for Computer Graphics and CAD, Springer Verlag, 2005.
- [6] F. Durante, E.P. Klement, C. Sempi and M. Ubeda-Flores, Measures of non- exchangeability for bivariate random vectors, Statist. Papers, 51 (3), 687-699, 2010.
- [7] T. Emura, S. Matsui and V. Rondeau, Survival Analysis with Correlated Endpoints, Joint Frailty-Copula Models, JSS Research Series in Statistics, Springer, 2019.
- [8] W. Feller, An Introduction to Probability Theory and its Applications, Wiley, 1965.
- [9] Y. Jun, Enjoy the joy of copulas: with a package copula, J. Stat. Softw. 21 (4), 1-21, 2007.
- [10] R.B. Nelsen, An Introduction to Copulas, Springer, 2007.
- [11] R.B. Nelsen, Extremes of nonexchangeability, Statist. Papers, 48 (2), 329-336, 2007.
- [12] D. Pfeifer and O. Ragulina, Adaptive Bernstein copulas and risk management, Mathematics, 8 (12), 1-22, 2020.
- [13] J.A. Rodriguez Lallena, Estudio de la compatibilidad y diseño de nuevas familias en la teoría de cópulas aplicaciones, PhD thesis, Universidad de Granada, 1992.
- [14] S. Saekaow and S. Tasena, Sobolev convergence of empirical Bernstein copulas, Hacet. J. Math. Stat. 48 (6), 1845-1858, 2019.
- [15] A. Sklar, Fonctions de repartition a n dimensions et leurs marges, Publ. Inst. Stat. Univ. Paris 8, 229-231, 1959.
- [16] L.H. Sun, X.W. Huang, M.S. Alqawba, J.M. Kim and T. Emura, Copula-based Markov Models for Time Series-Parametric Inference and Process Control, JSS Research Series in Statistics, Springer, 2020.
- [17] S.O. Susam, Parameter estimation of some Archimedean copulas based on minimum Cramér-von-Mises distance, J. Iran. Stat. Soc. (JIRSS) 19 (1), 163-183, 2020.
- [18] S.O. Susam and M.S. Erdogan, Plug-in estimation of dependence characteristics of Archimedean copula via Bézier curve, REVSTAT, 1-17, In Press.
- [19] S.O. Susam and B.H. Ucer, Testing independence for Archimedean copula based on Bernstein estimate of Kendall distribution function, J. Stat. Comput. Simul. 88 (13), 2589-2599, 2018.
- [20] S.O. Susam and B.H. Ucer, A goodness-of-fit test based on Bézier curve estimation of Kendall distribution, J. Stat. Comput. Simul. 90 (7), 1194-1215, 2020.
- [21] S.O. Susam and B.H. Ucer, On construction of Bernstein-Bézier type bivariate Archimedean copula, REVSTAT, 1-17, In Press.
- [22] M. Úbeda Flores, Introducción a la teoria de cópulas. Aplicaciones, Predoctoral Research Dissertation, Universidad de Almeria, 1998.
- [23] G. Weiß, Parameter estimation by maximum-likelihood and minimum-distance estimators: a simulation study, Comput. Statist. 26 (1), 31-54, 2011.
There are 23 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Statistics |
| Journal Section | Statistics |
| Authors | |
| Publication Date | April 1, 2022 |
| Published in Issue | Year 2022 Volume: 51 Issue: 2 |