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A new family of positive quadrant dependent bivariate distributions

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  • Lai, C. D.
  • Xie, M.

Abstract

Positive quadrant dependence (PQD) is a notion of bivariate dependence between two positively dependent random variables. Starting from the uniform representation of the Farlie-Gumbel-Morgenstern bivariate distribution, we derive and study a family of continuous bivariate distributions that possesses the PQD property. In particular, we show that this new parametric family of distributions can be ordered in the so-called "PQD order".

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:46:y:2000:i:4:p:359-364
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    References listed on IDEAS

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    1. Nelsen, Roger B., 1992. "On measures of association as measures of positive dependence," Statistics & Probability Letters, Elsevier, vol. 14(4), pages 269-274, July.
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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. Arjun Gupta & Johanna Orozco-Castañeda & Daya Nagar, 2011. "Non-central bivariate beta distribution," Statistical Papers, Springer, vol. 52(1), pages 139-152, February.
    3. Cerqueti, Roy & Costantini, Mauro & Lupi, Claudio, 2012. "A copula-based analysis of false discovery rate control under dependence assumptions," Economics & Statistics Discussion Papers esdp12065, University of Molise, Department of Economics.
    4. 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.
    5. 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.
    6. Fischer, Matthias J. & Klein, Ingo, 2004. "Constructing symmetric generalized FGM copulas by means of certain univariate distributions," Discussion Papers 61/2004, Friedrich-Alexander University Erlangen-Nuremberg, Chair of Statistics and Econometrics.
    7. Cuadras, Carles M. & Cuadras, Daniel, 2008. "Eigenanalysis on a bivariate covariance kernel," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2497-2507, November.
    8. Werner Hürlimann, 2017. "A comprehensive extension of the FGM copula," Statistical Papers, Springer, vol. 58(2), pages 373-392, June.
    9. 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.
    10. Mao, Tiantian & Yang, Fan, 2015. "Risk concentration based on Expectiles for extreme risks under FGM copula," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 429-439.
    11. Hakim Bekrizadeh & Babak Jamshidi, 2017. "A new class of bivariate copulas: dependence measures and properties," METRON, Springer;Sapienza Università di Roma, vol. 75(1), pages 31-50, April.

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