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A dependent bivariate t distribution with marginals on different degrees of freedom

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  • Jones, M. C.

Abstract

Let Z1,Z2 and W1,W2 be mutually independent random variables, each Zi following the standard normal distribution and Wi following the chi-squared distribution on ni degrees of freedom. Then, the pair of random variables , has the bivariate spherically symmetric t distribution; this has both marginals the same, namely Student's t distributions on n1 degrees of freedom. In this paper, we study the joint distribution of {, ,} where [nu]1=n1, [nu]2=n1+n2. This bivariate distribution has marginal distributions which are Student t distributions on different degrees of freedom if [nu]1[not equal to][nu]2. The marginals remain uncorrelated, as in the spherically symmetric case, but are also by no means independent.

Suggested Citation

  • Jones, M. C., 2002. "A dependent bivariate t distribution with marginals on different degrees of freedom," Statistics & Probability Letters, Elsevier, vol. 56(2), pages 163-170, January.
    • Handle: RePEc:eee:stapro:v:56:y:2002:i:2:p:163-170
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    Cited by:

    1. Dubey, Subodh & Bansal, Prateek & Daziano, Ricardo A. & Guerra, Erick, 2020. "A Generalized Continuous-Multinomial Response Model with a t-distributed Error Kernel," Transportation Research Part B: Methodological, Elsevier, vol. 133(C), pages 114-141.
    2. Ebrahimi, Nader & Hamedani, G.G. & Soofi, Ehsan S. & Volkmer, Hans, 2010. "A class of models for uncorrelated random variables," Journal of Multivariate Analysis, Elsevier, vol. 101(8), pages 1859-1871, September.
    3. Karoline Bax & Emanuele Taufer & Sandra Paterlini, 2022. "A generalized precision matrix for t-Student distributions in portfolio optimization," Papers 2203.13740, arXiv.org.
    4. Shaw, W.T. & Lee, K.T.A., 2008. "Bivariate Student t distributions with variable marginal degrees of freedom and independence," Journal of Multivariate Analysis, Elsevier, vol. 99(6), pages 1276-1287, July.
    5. S.T. Boris Choy & Cathy W.S. Chen & Edward M.H. Lin, 2014. "Bivariate asymmetric GARCH models with heavy tails and dynamic conditional correlations," Quantitative Finance, Taylor & Francis Journals, vol. 14(7), pages 1297-1313, July.
    6. José María Sarabia & Vanesa Jordá & Faustino Prieto & Montserrat Guillén, 2020. "Multivariate Classes of GB2 Distributions with Applications," Mathematics, MDPI, vol. 9(1), pages 1-21, December.
    7. Subodh Dubey & Prateek Bansal & Ricardo A. Daziano & Erick Guerra, 2019. "A Generalized Continuous-Multinomial Response Model with a t-distributed Error Kernel," Papers 1904.08332, arXiv.org, revised Jan 2020.

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