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Some properties and generalizations of multivariate Eyraud-Gumbel-Morgenstern distributions

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  • Cambanis, Stamatis

Abstract

The admissible values of the coefficient in a bivariate Eyraud-Gumbel-Morgenstern (EGM) distribution are found. For multivariate EGM distributions necessary and sufficient conditions are given for its coefficients, and its conditional distributions are found and shown to belong to a family of distributions further extending the multivariate EGM family.

Suggested Citation

  • Cambanis, Stamatis, 1977. "Some properties and generalizations of multivariate Eyraud-Gumbel-Morgenstern distributions," Journal of Multivariate Analysis, Elsevier, vol. 7(4), pages 551-559, December.
    • Handle: RePEc:eee:jmvana:v:7:y:1977:i:4:p:551-559
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    Cited by:

    1. Radu Tunaru, 2015. "Model Risk in Financial Markets:From Financial Engineering to Risk Management," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 9524, August.
    2. Pawlak, Jacek & Polak, John W. & Sivakumar, Aruna, 2017. "A framework for joint modelling of activity choice, duration, and productivity while travelling," Transportation Research Part B: Methodological, Elsevier, vol. 106(C), pages 153-172.
    3. Tang, Qihe & Vernic, Raluca, 2007. "The impact on ruin probabilities of the association structure among financial risks," Statistics & Probability Letters, Elsevier, vol. 77(14), pages 1522-1525, August.
    4. Jovanović, Mario, 2011. "Does Monetary Policy Affect Stock Market Uncertainty? – Empirical Evidence from the United States," Ruhr Economic Papers 240, RWI - Leibniz-Institut für Wirtschaftsforschung, Ruhr-University Bochum, TU Dortmund University, University of Duisburg-Essen.
    5. Hashorva, E. & Hüsler, J., 1999. "Extreme Values in FGM Random Sequences," Journal of Multivariate Analysis, Elsevier, vol. 68(2), pages 212-225, February.
    6. Li, Jinzhu, 2022. "Asymptotic results on marginal expected shortfalls for dependent risks," Insurance: Mathematics and Economics, Elsevier, vol. 102(C), pages 146-168.
    7. Saminger-Platz Susanne & Kolesárová Anna & Šeliga Adam & Mesiar Radko & Klement Erich Peter, 2021. "New results on perturbation-based copulas," Dependence Modeling, De Gruyter, vol. 9(1), pages 347-373, January.
    8. Mario Jovanovic, 2011. "Does Monetary Policy Affect Stock Market Uncertainty? – Empirical Evidence from the United States," Ruhr Economic Papers 0240, Rheinisch-Westfälisches Institut für Wirtschaftsforschung, Ruhr-Universität Bochum, Universität Dortmund, Universität Duisburg-Essen.
    9. Hashorva, Enkelejd, 2001. "Asymptotic results for FGM random sequences," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 417-425, October.
    10. Okolewski, A. & Kaluszka, M., 2015. "Stability of expected L-statistics against weak dependence of observations," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 157-164.
    11. Genest, Christian & Hron, Karel & Nešlehová, Johanna G., 2023. "Orthogonal decomposition of multivariate densities in Bayes spaces and relation with their copula-based representation," Journal of Multivariate Analysis, Elsevier, vol. 198(C).
    12. Ibragimov, Rustam & Prokhorov, Artem, 2016. "Heavy tails and copulas: Limits of diversification revisited," Economics Letters, Elsevier, vol. 149(C), pages 102-107.
    13. Sharakhmetov, Sh. & Ibragimov, R., 2002. "A Characterization of Joint Distribution of Two-Valued Random Variables and Its Applications," Journal of Multivariate Analysis, Elsevier, vol. 83(2), pages 389-408, November.
    14. Chandra Bhat & Ipek Sener, 2009. "A copula-based closed-form binary logit choice model for accommodating spatial correlation across observational units," Journal of Geographical Systems, Springer, vol. 11(3), pages 243-272, September.
    15. Blier-Wong, Christopher & Cossette, Hélène & Marceau, Etienne, 2023. "Risk aggregation with FGM copulas," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 102-120.
    16. 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.
    17. Šeliga Adam & Kauers Manuel & Saminger-Platz Susanne & Mesiar Radko & Kolesárová Anna & Klement Erich Peter, 2021. "Polynomial bivariate copulas of degree five: characterization and some particular inequalities," Dependence Modeling, De Gruyter, vol. 9(1), pages 13-42, January.
    18. repec:zbw:rwirep:0240 is not listed on IDEAS
    19. Barbiero, A., 2019. "A bivariate count model with discrete Weibull margins," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 156(C), pages 91-109.
    20. Ying Zhang & Chuancun Yin, 2014. "A new multivariate dependence measure based on comonotonicity," Papers 1410.7845, arXiv.org.
    21. Blier-Wong, Christopher & Cossette, Hélène & Marceau, Etienne, 2022. "Stochastic representation of FGM copulas using multivariate Bernoulli random variables," Computational Statistics & Data Analysis, Elsevier, vol. 173(C).
    22. Cui, Hengxin & Tan, Ken Seng & Yang, Fan & Zhou, Chen, 2022. "Asymptotic analysis of portfolio diversification," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 302-325.

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