A Bayesian Approach for Stable Distributions: Some Computational Aspects

Jorge A. Achcar; Sílvia R. C. Lopes; Josmar Mazucheli; Raquel R. Linhares

doi:10.4236/ojs.2013.34031

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A Bayesian Approach for Stable Distributions: Some Computational Aspects

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DOI: 10.4236/ojs.2013.34031 3,500 Downloads 5,005 Views Citations

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Jorge A. Achcar, Sílvia R. C. Lopes, Josmar Mazucheli, Raquel R. Linhares

Affiliation(s)

Departament of Statistics, UEM, Maringá, Brazil.
Mathematical Institute, UFRGS, Porto Alegre, Brazil.
Medical School, USP, Ribeir?o Preto, Brazil.

ABSTRACT

In this work, we study some computational aspects for the Bayesian analysis involving stable distributions. It is well known that, in general, there is no closed form for the probability density function of stable distributions. However, the use of a latent or auxiliary random variable facilitates to obtain any posterior distribution when being related to stable distributions. To show the usefulness of the computational aspects, the methodology is applied to two examples: one is related to daily price returns of Abbey National shares, considered in [1], and the other is the length distribution analysis of coding and non-coding regions in a Homo sapiens chromosome DNA sequence, considered in [2]. Posterior summaries of interest are obtained using the OpenBUGS software.

KEYWORDS

Stable Laws; Bayesian Analysis; DNA Sequences; MCMC Methods; OpenBUGS Software

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

J. Achcar, S. Lopes, J. Mazucheli and R. Linhares, "A Bayesian Approach for Stable Distributions: Some Computational Aspects," Open Journal of Statistics, Vol. 3 No. 4, 2013, pp. 268-277. doi: 10.4236/ojs.2013.34031.

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