Brazilian Journal of Probability and Statistics

A large class of new bivariate copulas and their properties

Zahra Sharifonnasabi, Mohammad Hossein Alamatsaz, and Iraj Kazemi

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

In this paper, we shall construct a large class of new bivariate copulas. This class happens to contain several known classes of copulas, such as Farlie–Gumbel–Morgenstern, Ali–Mikhail–Haq and Barnett–Gumbel, as its especial members. It is shown that the proposed copulas improve the range of values of correlation coefficient and thus they are more applicable in data modeling. We shall also reveal that the dependent properties of the base copula are preserved by the generated copula under certain conditions. Several members of the new class are introduced as instances and their range of correlation coefficients are computed.

Article information

Source
Braz. J. Probab. Stat., Volume 32, Number 3 (2018), 497-524.

Dates
Received: June 2015
Accepted: January 2017
First available in Project Euclid: 8 June 2018

Permanent link to this document
https://projecteuclid.org/euclid.bjps/1528444869

Digital Object Identifier
doi:10.1214/17-BJPS351

Mathematical Reviews number (MathSciNet)
MR3812379

Zentralblatt MATH identifier
06930036

Keywords
FGM copulas stochastic dependence tail dependence Spearman’s $\rho$

Citation

Sharifonnasabi, Zahra; Alamatsaz, Mohammad Hossein; Kazemi, Iraj. A large class of new bivariate copulas and their properties. Braz. J. Probab. Stat. 32 (2018), no. 3, 497--524. doi:10.1214/17-BJPS351. https://projecteuclid.org/euclid.bjps/1528444869


Export citation

References

  • Amblard, C. and Girard, S. (2002). Symmetry and dependence properties within a semiparametric family of bivariate copulas. Nonparametric Statistics 14, 715–727.
  • Amblard, C. and Girard, S. (2009). A new extension of bivariate FGM copulas. Metrika 70, 1–17.
  • Amini, M., Jabbari, H. and Mohtashami Borzadaran, G. R. (2011). Aspects of dependence in generalized Farlie–Gumbel–Morgenstern distribution. Communications in Statistics-Simulation and Computation 40, 1192–1205.
  • Bairamov, I. and Kotz, S. (2002). Dependence structure and symmetry of Huang–Kotz FGM distributions and their extensions. Metrika 56, 55–72.
  • Cook, R. D. and Johnson, M. E. (1986). Generalized Burr–Pareto-logistic distributions with applications to a uranium exploration data set. Technometrics 28, 123–131.
  • Delahorra, J. and Fernandez, C. (1995). Sensitivity to prior independence via Farlie–Gumbel–Morgenstern model. Communications in Statistics-Theory Methods 24, 987–996.
  • Grane, G. J. (2009). Copulas for credit derviative pricing and other application. Ph.D. thesis.
  • Huang, J. S. and Kotz, S. (1999). Modifications of the Farlie–Gumbel–Morgenstern distribution. A tough hill to climb. Metrika 49, 135–145.
  • Klein, I. and Christa, F. (2011). Families of copulas closed under the construction of generalized linear means. IWQW discussion paper series, No. 04/2011.
  • Lin, G. D. (1987). Relationships between two extensions of Farlie–Gumbel–Morgenstern distribution. Annals of the Institute of Statistical Mathematics 39, 129–140.
  • Nelsen, R. B. (2006). An Introduction to Copulas. New York: Springer.
  • Sklar, A. (1959). Functions de repartition a n dimensions et leurs marges. Publication de Institut Statistique de Universite de Paris 8, 229–231.
  • Tolley, H. D. and Norman, J. E. (1979). Time on trial estimates with bivariate risks. Biometrika 66, 285–291.