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Box–Cox elliptical distributions with application

Author

Listed:
  • Raúl Alejandro Morán-Vásquez

    (University of Antioquia)

  • Silvia L. P. Ferrari

    (University of São Paulo)

Abstract

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.

Suggested Citation

  • Raúl Alejandro Morán-Vásquez & Silvia L. P. Ferrari, 2019. "Box–Cox elliptical distributions with application," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(5), pages 547-571, July.
    • Handle: RePEc:spr:metrik:v:82:y:2019:i:5:d:10.1007_s00184-018-0682-z
    DOI: 10.1007/s00184-018-0682-z
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    References listed on IDEAS

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    1. Kano, Y., 1994. "Consistency Property of Elliptic Probability Density Functions," Journal of Multivariate Analysis, Elsevier, vol. 51(1), pages 139-147, October.
    2. Horrace, William C., 2005. "Some results on the multivariate truncated normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 94(1), pages 209-221, May.
    3. Vlasios Voudouris & Robert Gilchrist & Robert Rigby & John Sedgwick & Dimitrios Stasinopoulos, 2012. "Modelling skewness and kurtosis with the BCPE density in GAMLSS," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(6), pages 1279-1293, November.
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