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A Truncated Bivariate t Distribution

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  • Nadarajah Saralees

    (School of Mathematics, University of Manchester, Manchester M60 1QD, United Kingdom)

Abstract

A truncated version of the bivariate t distribution is introduced. Unlike the t distribution, this possesses finite moments of all orders and could, therefore, be a better model for real-world situations, as it becomes possible to incorporate always available knowledge about the range of variability of the considered aspect into the model. Using the usual t distribution, this knowledge has to be abandoned and additionally the purely mathematical problems of infinite moments occurs. One such situation is discussed. Explicit expressions for the moments of the truncated distribution are also derived.

Suggested Citation

  • Nadarajah Saralees, 2007. "A Truncated Bivariate t Distribution," Stochastics and Quality Control, De Gruyter, vol. 22(2), pages 303-313, January.
    • Handle: RePEc:bpj:ecqcon:v:22:y:2007:i:2:p:303-313:n:12
    DOI: 10.1515/EQC.2007.303
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    References listed on IDEAS

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    1. Chib, Siddharta & Osiewalski, Jacek & Steel, Mark F. J., 1991. "Posterior inference on the degrees of freedom parameter in multivariate-t regression models," Economics Letters, Elsevier, vol. 37(4), pages 391-397, December.
    2. Fiorentini, Gabriele & Sentana, Enrique & Calzolari, Giorgio, 2003. "Maximum Likelihood Estimation and Inference in Multivariate Conditionally Heteroscedastic Dynamic Regression Models with Student t Innovations," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(4), pages 532-546, October.
    3. Osiewalski, Jacek & Steel, Mark F. J., 1993. "Robust bayesian inference in elliptical regression models," Journal of Econometrics, Elsevier, vol. 57(1-3), pages 345-363.
    4. Paul Glasserman & Philip Heidelberger & Perwez Shahabuddin, 2002. "Portfolio Value‐at‐Risk with Heavy‐Tailed Risk Factors," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 239-269, July.
    5. Ohtani, Kazuhiro & Hasegawa, Hikaru, 1993. "On Small Sample Properties of R2 in a Linear Regression Model with Multivariate t Errors and Proxy Variables," Econometric Theory, Cambridge University Press, vol. 9(3), pages 504-515, June.
    6. Chib, Siddhartha & Winkelmann, Rainer, 2001. "Markov Chain Monte Carlo Analysis of Correlated Count Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(4), pages 428-435, October.
    7. Liu, Chuanhai & Rubin, Donald B., 1996. "Markov-Normal analysis of iterative simulations before their convergence," Journal of Econometrics, Elsevier, vol. 75(1), pages 69-78, November.
    8. Lien, Da-Hsiang Donald, 1985. "Moments of truncated bivariate log-normal distributions," Economics Letters, Elsevier, vol. 19(3), pages 243-247.
    9. Barton H. Hamilton, 1999. "HMO selection and Medicare costs: Bayesian MCMC estimation of a robust panel data tobit model with survival," Health Economics, John Wiley & Sons, Ltd., vol. 8(5), pages 403-414, August.
    10. Frees, Edward W. & Wang, Ping, 2006. "Copula credibility for aggregate loss models," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 360-373, April.
    11. Chib, Siddhartha, 1992. "Bayes inference in the Tobit censored regression model," Journal of Econometrics, Elsevier, vol. 51(1-2), pages 79-99.
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    Cited by:

    1. Saieed Ateya & Elham Madhagi, 2013. "On multivariate truncated generalized Cauchy distribution," Statistical Papers, Springer, vol. 54(3), pages 879-897, August.
    2. Arismendi, J.C., 2013. "Multivariate truncated moments," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 41-75.

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