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A Compound Positively Dependent Farlie-Gumbel-Morgenstern Bivariate Copula

Year 2022, Volume: 14 Issue: 1, 11 - 16, 31.07.2022

Abstract

In this study, we propose a two parameter Farlie-Gumbel-Morgenstern (FGM) copula that maintains membership in the family in a way while adding the extra dependence parameter to the model by using the compound method. Also, we assess the performance of the new compound FGM copula among all the most used two-parameter families of FGM copulas. The new copula performs best for the real data having moderate dependence structure.

References

  • Bairamov, I. and Bairamov, K. (2013). From the Huang Kotz FGM distribution to Baker's bivariate distribution. Journal of Multivariate Analysis, 113, 106-115.
  • Berg, D. (2009). Copula goodness-of-fit testing: an overview and power comparison. The European Journal of Finance, 15, 675-701.
  • Cossette, H., Cote, M.P., Marceau, E. and Moutanabbir, K. (2013). Multivariate distribution defined with Farlie-Gumbel-Morgenstern copula and mixed Erlang marginals: Aggregation and capital allocation. Insurance: Mathematics and Economics, 52(3), 560-572.
  • Farlie, D.J.G. (1960). The performance of some correlation coefficients for a general bivariate distribution. Biometrika, 47 (3-4), 307-23.
  • Gumbel, E. (1960). Bivariate exponential distributions. Journal of the American Statistical Association, 55(292), 698-707.
  • Huang, J.S. and Kotz, S. (1984). Correlation structure in iterated Farlie-Gumbel-Morgenstern distributions. Biometrika, 71(3), 633-636.
  • Huang, J.S. and Kotz, S. (1999). Modifications of the Farlie-Gumbel-Morgenstern distributions. A tough hill to climb. Metrika, 49(2),135-45.
  • Kelner, M., Landsman, Z. and Makov, U.E. (2021). Compound Archimedean copulas. International Journal of Statistics and Probability, 10(3), 126-126.
  • Lai, C.D. and Xie, M. (2000). A new family of positive quadrant dependent bivariate distributions. Statistics & Probability Letters, 46, 359-634.
  • Lu, L. and Ghosh, S.K. (2021). Nonparametric estimation and testing for positive quadrant dependent bivariate copula. Journal of Business and Economic Statistics, In Press.
  • Morgenstern, D. (1956). Einfache beispiele zweidimensionaler verteilungen. Mitteilingsblatt Feur Mathematische Statistik, 8, 234-235.
  • Navarro, J. and Durante, F. (2017). Copula-based representations for the reliability of the residual lifetimes of coherent systems with dependent components. Journal of Multivariate Analysis, 158, 87-102.
  • Navarro, J., Ruiz, J.M. and Sandoval, C.J. (2007). Properties of coherent systems with dependent components. Communications in Statistics-Theory and Methods, 36, 175-191.
  • Patton, A. J. (2006). Estimation of multivariate models for time series of possibly different lengths. Journal of Applied Econometrics, 21(2), 147-173.
  • Sklar, A. (1959). Fonctions de répartition à n dimensions et leurs marges. Publications de l'Institut Statistique de l'Université de Paris, 8, 229-231.
Year 2022, Volume: 14 Issue: 1, 11 - 16, 31.07.2022

Abstract

References

  • Bairamov, I. and Bairamov, K. (2013). From the Huang Kotz FGM distribution to Baker's bivariate distribution. Journal of Multivariate Analysis, 113, 106-115.
  • Berg, D. (2009). Copula goodness-of-fit testing: an overview and power comparison. The European Journal of Finance, 15, 675-701.
  • Cossette, H., Cote, M.P., Marceau, E. and Moutanabbir, K. (2013). Multivariate distribution defined with Farlie-Gumbel-Morgenstern copula and mixed Erlang marginals: Aggregation and capital allocation. Insurance: Mathematics and Economics, 52(3), 560-572.
  • Farlie, D.J.G. (1960). The performance of some correlation coefficients for a general bivariate distribution. Biometrika, 47 (3-4), 307-23.
  • Gumbel, E. (1960). Bivariate exponential distributions. Journal of the American Statistical Association, 55(292), 698-707.
  • Huang, J.S. and Kotz, S. (1984). Correlation structure in iterated Farlie-Gumbel-Morgenstern distributions. Biometrika, 71(3), 633-636.
  • Huang, J.S. and Kotz, S. (1999). Modifications of the Farlie-Gumbel-Morgenstern distributions. A tough hill to climb. Metrika, 49(2),135-45.
  • Kelner, M., Landsman, Z. and Makov, U.E. (2021). Compound Archimedean copulas. International Journal of Statistics and Probability, 10(3), 126-126.
  • Lai, C.D. and Xie, M. (2000). A new family of positive quadrant dependent bivariate distributions. Statistics & Probability Letters, 46, 359-634.
  • Lu, L. and Ghosh, S.K. (2021). Nonparametric estimation and testing for positive quadrant dependent bivariate copula. Journal of Business and Economic Statistics, In Press.
  • Morgenstern, D. (1956). Einfache beispiele zweidimensionaler verteilungen. Mitteilingsblatt Feur Mathematische Statistik, 8, 234-235.
  • Navarro, J. and Durante, F. (2017). Copula-based representations for the reliability of the residual lifetimes of coherent systems with dependent components. Journal of Multivariate Analysis, 158, 87-102.
  • Navarro, J., Ruiz, J.M. and Sandoval, C.J. (2007). Properties of coherent systems with dependent components. Communications in Statistics-Theory and Methods, 36, 175-191.
  • Patton, A. J. (2006). Estimation of multivariate models for time series of possibly different lengths. Journal of Applied Econometrics, 21(2), 147-173.
  • Sklar, A. (1959). Fonctions de répartition à n dimensions et leurs marges. Publications de l'Institut Statistique de l'Université de Paris, 8, 229-231.
There are 15 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Selim Orhun Susam 0000-0001-7896-9055

Publication Date July 31, 2022
Acceptance Date December 20, 2021
Published in Issue Year 2022 Volume: 14 Issue: 1

Cite

APA Susam, S. O. (2022). A Compound Positively Dependent Farlie-Gumbel-Morgenstern Bivariate Copula. Istatistik Journal of The Turkish Statistical Association, 14(1), 11-16.
AMA Susam SO. A Compound Positively Dependent Farlie-Gumbel-Morgenstern Bivariate Copula. IJTSA. July 2022;14(1):11-16.
Chicago Susam, Selim Orhun. “A Compound Positively Dependent Farlie-Gumbel-Morgenstern Bivariate Copula”. Istatistik Journal of The Turkish Statistical Association 14, no. 1 (July 2022): 11-16.
EndNote Susam SO (July 1, 2022) A Compound Positively Dependent Farlie-Gumbel-Morgenstern Bivariate Copula. Istatistik Journal of The Turkish Statistical Association 14 1 11–16.
IEEE S. O. Susam, “A Compound Positively Dependent Farlie-Gumbel-Morgenstern Bivariate Copula”, IJTSA, vol. 14, no. 1, pp. 11–16, 2022.
ISNAD Susam, Selim Orhun. “A Compound Positively Dependent Farlie-Gumbel-Morgenstern Bivariate Copula”. Istatistik Journal of The Turkish Statistical Association 14/1 (July 2022), 11-16.
JAMA Susam SO. A Compound Positively Dependent Farlie-Gumbel-Morgenstern Bivariate Copula. IJTSA. 2022;14:11–16.
MLA Susam, Selim Orhun. “A Compound Positively Dependent Farlie-Gumbel-Morgenstern Bivariate Copula”. Istatistik Journal of The Turkish Statistical Association, vol. 14, no. 1, 2022, pp. 11-16.
Vancouver Susam SO. A Compound Positively Dependent Farlie-Gumbel-Morgenstern Bivariate Copula. IJTSA. 2022;14(1):11-6.