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Multivariate Exponential Power Distributions as Mixtures of Normal Distributions with Bayesian Applications
Article de revue   Avec comité de lecture

Multivariate Exponential Power Distributions as Mixtures of Normal Distributions with Bayesian Applications

E. Gómez-Sánchez-Manzano, M. A. Gómez-Villegas et J. M. Marín
Communications in statistics. Theory and methods, Vol.37(6), pp.972-985
11/02/2008
DOI: https://doi.org/10.1080/03610920701762754

Résumé

Elliptical distribution Elliptically contoured distribution Gibbs sampler Hierarchical Bayesian model Montecarlo methods Multivariate exponential power distribution Primary 62F15 Scale mixture of normal distributions Secodnary 62E17 Stable distribution
This paper shows that a multivariate exponential power distribution is a scale mixture of normal distributions, with respect to a probability distribution function, when its kurtosis parameter belongs to the interval (0, 1]. The corresponding mixing probability distribution function is presented. This result is used to design, through a Bayesian hierarchical model, an algorithm to generate samples of the posterior distribution; this is applied to a problem of quantitative genetics.

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