Box–Cox elliptical distributions with application
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We propose and study the class of Box–Cox elliptical distributions. It provides alternative distributions for modeling multivariate positive, marginally skewed and possibly heavy-tailed data. This new class of distributions has as a special case the class of log-elliptical distributions, and reduces to the Box–Cox symmetric class of distributions in the univariate setting. The parameters are interpretable in terms of quantiles and relative dispersions of the marginal distributions and of associations between pairs of variables. The relation between the scale parameters and quantiles makes the Box–Cox elliptical distributions attractive for regression modeling purposes. Applications to data on vitamin intake are presented and discussed.
KeywordsBox–Cox symmetric distributions Box–Cox transformation Elliptical distribution Gibbs sampling Truncated distribution
We thank José Eduardo Corrente for providing the data used in this study. Funding was provided by Conselho Nacional de Desenvolvimento Científico e Tecnológico—CNPq (Grant No. 304388-2014-9) and Fundação de Amparo à Pesquisa do Estado de São Paulo—FAPESP (Grant No. 2012/21788-2). The first author received Ph.D. scholarships from Coordenação de Aperfeiçoamento de Pessoal de Nível Superior—CAPES—and CNPq. We are thankful to the Editor, Associate Editor and the anonymous reviewers for their helpful comments and suggestions.
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