On the matrix-variate generalized hyperbolic distribution and its Bayesian applications |
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| Authors: | L. Thabane M. Safiul Haq |
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| Affiliation: | 1. Department of Clinical Epidemiology and Biostatistics , McMaster University, Centre for Evaluation of Medicines , 105 Main Street East, Level P1, Hamilton, Ontario, Canada , L8N 1G6thabanl@mcmaster.ca;3. Department of Statistical and Actuarial Sciences , University of Western Ontario , London, Ontario, Canada , N6A 5B7 |
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| Abstract: | In the first part of the paper, we introduce the matrix-variate generalized hyperbolic distribution by mixing the matrix normal distribution with the matrix generalized inverse Gaussian density. The p-dimensional generalized hyperbolic distribution of [Barndorff-Nielsen, O. (1978). Hyperbolic distributions and distributions on hyperbolae. Scand. J. Stat., 5, 151–157], the matrix-T distribution and many well-known distributions are shown to be special cases of the new distribution. Some properties of the distribution are also studied. The second part of the paper deals with the application of the distribution in the Bayesian analysis of the normal multivariate linear model. |
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| Keywords: | Matrix-variate generalized hyperbolic distribution Matrix normal distribution Matrix generalized inverse Gaussian distribution Normal multivariate linear model Posterior and prediction distributions |
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