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New generalized Farlie-Gumbel-Morgenstern distributions and concomitants of order statistics

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  • I. Bairamov
  • S. Kotz
  • M. Bekci

Abstract

We consider a generalization of the bivariate Farlie-Gumbel-Morgenstern (FGM) distribution by introducing additional parameters. For the generalized FGM distribution, the admissible range of the association parameter allowing positive quadrant dependence property is shown. Distributional properties of concomitants for this generalized FGM distribution are studied. Recurrence relations between moments of concomitants are presented.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:japsta:v:28:y:2001:i:5:p:521-536
    DOI: 10.1080/02664760120047861
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. 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.
    2. Gebizlioglu, Omer L. & Yagci, Banu, 2008. "Tolerance intervals for quantiles of bivariate risks and risk measurement," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1022-1027, June.
    3. Indranil Ghosh, 2017. "Bivariate Kumaraswamy Models via Modified FGM Copulas: Properties and Applications," JRFM, MDPI, vol. 10(4), pages 1-13, November.
    4. Jiang, Jun & Tang, Qihe, 2011. "The product of two dependent random variables with regularly varying or rapidly varying tails," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 957-961, August.
    5. 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.
    6. Komelj, Janez & Perman, Mihael, 2010. "Joint characteristic functions construction via copulas," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 137-143, October.
    7. Woo, Jae-Kyung & Cheung, Eric C.K., 2013. "A note on discounted compound renewal sums under dependency," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 170-179.
    8. Filippo Domma & Sabrina Giordano, 2013. "A copula-based approach to account for dependence in stress-strength models," Statistical Papers, Springer, vol. 54(3), pages 807-826, August.
    9. Shih, Jia-Han & Emura, Takeshi, 2021. "On the copula correlation ratio and its generalization," Journal of Multivariate Analysis, Elsevier, vol. 182(C).
    10. Kahkashan Afrin & Ashif S Iquebal & Mostafa Karimi & Allyson Souris & Se Yoon Lee & Bani K Mallick, 2020. "Directionally dependent multi-view clustering using copula model," PLOS ONE, Public Library of Science, vol. 15(10), pages 1-18, October.
    11. Savita Jain & Suresh K. Sharma & Kanchan Jain, 2022. "Using Copulas for Bayesian Meta-analysis," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 14(1), pages 23-41, April.

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