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Gómez-Sánchez-Manzano, E.; Gómez-Villegas, M. A.; Marín, J. M.

Multivariate exponential power distributions as mixtures of normal distributions with Bayesian applications. (English) Zbl 1135.62041

Commun. Stat., Theory Methods 37, No. 6, 972-985 (2008).
Summary: 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.

Cited in 23 Documents

MSC:

62H10 Multivariate distribution of statistics
62F15 Bayesian inference
62E17 Approximations to statistical distributions (nonasymptotic)
62H05 Characterization and structure theory for multivariate probability distributions; copulas
65C05 Monte Carlo methods

Keywords:

elliptical distribution; elliptically contoured distribution; Gibbs sampler; hierarchical Bayesian model; multivariate exponential power distribution; scale mixture of normal distributions; stable distribution; mutational effects of genetic quantiative traits

Software:

STABLE; R; boa
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Full Text: DOI Link

References:

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