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Family of multivariate generalized t distributions

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  • Arslan, Olcay

Abstract

In this paper, we introduce a new family of multivariate distributions as the scale mixture of the multivariate power exponential distribution introduced by Gómez et al. (Comm. Statist. Theory Methods 27(3) (1998) 589) and the inverse generalized gamma distribution. Since the resulting family includes the multivariate t distribution and the multivariate generalization of the univariate GT distribution introduced by McDonald and Newey (Econometric Theory 18 (11) (1988) 4039) we call this family as the "multivariate generalized t-distributions family", or MGT for short. We show that this family of distributions belongs to the elliptically contoured distributions family, and investigate the properties. We give the stochastic representation of a random variable distributed as a multivariate generalized t distribution. We give the marginal distribution, the conditional distribution and the distribution of the quadratic forms. We also investigate the other properties, such as, asymmetry, kurtosis and the characteristic function.

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  • Arslan, Olcay, 2004. "Family of multivariate generalized t distributions," Journal of Multivariate Analysis, Elsevier, vol. 89(2), pages 329-337, May.
    • Handle: RePEc:eee:jmvana:v:89:y:2004:i:2:p:329-337
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    1. Butler, Richard J, et al, 1990. "Robust and Partially Adaptive Estimation of Regression Models," The Review of Economics and Statistics, MIT Press, vol. 72(2), pages 321-327, May.
    2. Arellano-Valle, Reinaldo B. & Bolfarine, Heleno, 1995. "On some characterizations of the t-distribution," Statistics & Probability Letters, Elsevier, vol. 25(1), pages 79-85, October.
    3. McDonald, James B & Butler, Richard J, 1987. "Some Generalized Mixture Distributions with an Application to Unemployment Duration," The Review of Economics and Statistics, MIT Press, vol. 69(2), pages 232-240, May.
    4. Newey, Whitney K., 1988. "Adaptive estimation of regression models via moment restrictions," Journal of Econometrics, Elsevier, vol. 38(3), pages 301-339, July.
    5. McDonald, James B. & Newey, Whitney K., 1988. "Partially Adaptive Estimation of Regression Models via the Generalized T Distribution," Econometric Theory, Cambridge University Press, vol. 4(3), pages 428-457, December.
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    1. Tata Subba Rao & Granville Tunnicliffe Wilson & Andrew Harvey & Rutger-Jan Lange, 2017. "Volatility Modeling with a Generalized t Distribution," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(2), pages 175-190, March.
    2. Victor Korolev, 2023. "Analytic and Asymptotic Properties of the Generalized Student and Generalized Lomax Distributions," Mathematics, MDPI, vol. 11(13), pages 1-27, June.
    3. Arslan, Olcay, 2005. "A new class of multivariate distributions: Scale mixture of Kotz-type distributions," Statistics & Probability Letters, Elsevier, vol. 75(1), pages 18-28, November.
    4. Fung, Thomas & Seneta, Eugene, 2008. "A characterisation of scale mixtures of the uniform distribution," Statistics & Probability Letters, Elsevier, vol. 78(17), pages 2883-2888, December.
    5. Wang, Joanna J.J., 2012. "On asymmetric generalised t stochastic volatility models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(11), pages 2079-2095.
    6. Adcock, C J & Meade, N, 2017. "Using parametric classification trees for model selection with applications to financial risk management," European Journal of Operational Research, Elsevier, vol. 259(2), pages 746-765.
    7. Trottini, Mario & Muralidhar, Krish & Sarathy, Rathindra, 2011. "Maintaining tail dependence in data shuffling using t copula," Statistics & Probability Letters, Elsevier, vol. 81(3), pages 420-428, March.
    8. Qian, Hang, 2009. "Estimating SUR Tobit Model while errors are gaussian scale mixtures: with an application to high frequency financial data," MPRA Paper 31509, University Library of Munich, Germany.

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