On the matrix-variate generalized hyperbolic distribution and its Bayesian applications. (English) Zbl 1055.62063
Summary: 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 O. Barndorff-Nielsen [Scand. J. Stat., Theory Appl. 5, 151–157 (1978; Zbl 0386.60018)], 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.
MSC:
| 62H05 | Characterization and structure theory for multivariate probability distributions; copulas |
| 62F15 | Bayesian inference |
| 62H12 | Estimation in multivariate analysis |
Keywords:
matrix-variate generalized hyperbolic distribution; matrix normal distribution; matrix generalized inverse Gaussian distribution; normal multivariate linear model; posterior and prediction distributionCitations:
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