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From the Huang–Kotz FGM distribution to Baker’s bivariate distribution

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  • Bairamov, I.
  • Bayramoglu, K.

Abstract

Huang and Kotz (1999) [17] considered a modification of the Farlie–Gumbel–Morgenstern (FGM) distribution, introducing additional parameters, and paved the way for many research papers on modifications of FGM distributions allowing high correlation. The first part of the present paper is a review of recent developments on bivariate Huang–Kotz FGM distributions and their extensions. In the second part a class of new bivariate distributions based on Baker’s system of bivariate distributions is considered. It is shown that for a model of a given order, this class of distributions with fixed marginals which are based on pairs of order statistics constructed from the bivariate sample observations of dependent random variables allows higher correlation than Baker’s system. It also follows that under certain conditions determined by Lin and Huang (2010) [21], the correlation for these systems converges to the maximum Fréchet–Hoeffding upper bound as the sample size tends to infinity.

Suggested Citation

  • Bairamov, I. & Bayramoglu, K., 2013. "From the Huang–Kotz FGM distribution to Baker’s bivariate distribution," Journal of Multivariate Analysis, Elsevier, vol. 113(C), pages 106-115.
    • Handle: RePEc:eee:jmvana:v:113:y:2013:i:c:p:106-115
    DOI: 10.1016/j.jmva.2011.03.001
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    References listed on IDEAS

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    1. Baker, Rose, 2008. "An order-statistics-based method for constructing multivariate distributions with fixed marginals," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2312-2327, November.
    2. I. Bairamov & S. Kotz & M. Bekci, 2001. "New generalized Farlie-Gumbel-Morgenstern distributions and concomitants of order statistics," Journal of Applied Statistics, Taylor & Francis Journals, vol. 28(5), pages 521-536.
    3. Rodríguez-Lallena, José Antonio & Úbeda-Flores, Manuel, 2004. "A new class of bivariate copulas," Statistics & Probability Letters, Elsevier, vol. 66(3), pages 315-325, February.
    4. Matthias Fischer & Ingo Klein, 2007. "Constructing Generalized FGM Copulas by Means of Certain Univariate Distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 65(2), pages 243-260, February.
    5. Lai, C. D. & Xie, M., 2000. "A new family of positive quadrant dependent bivariate distributions," Statistics & Probability Letters, Elsevier, vol. 46(4), pages 359-364, February.
    6. Lin, G.D. & Huang, J.S., 2010. "A note on the maximum correlation for Baker's bivariate distributions with fixed marginals," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2227-2233, October.
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    Cited by:

    1. Guo, Nan & Wang, Fang & Yang, Jingping, 2017. "Remarks on composite Bernstein copula and its application to credit risk analysis," Insurance: Mathematics and Economics, Elsevier, vol. 77(C), pages 38-48.
    2. Gulder Kemalbay & Ismihan Bayramoglu (Bairamov), 2015. "Joint distribution of new sample rank of bivariate order statistics," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(10), pages 2280-2289, October.
    3. Jia-Han Shih & Takeshi Emura, 2018. "Likelihood-based inference for bivariate latent failure time models with competing risks under the generalized FGM copula," Computational Statistics, Springer, vol. 33(3), pages 1293-1323, September.

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