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Modelling Directional Dispersion Through Hyperspherical Log- Splines

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Author Info

  • J.T.A.S. Ferreira

    (University of Warwick)

  • M.F.J. Steel

    (University of Warwick)

Abstract

We introduce the directionally dispersed class of multivariate distributions, a generalisation of the elliptical class. By allowing dispersion of multivariate random variables to vary with direction it is possible to generate a very wide and flexible class of distributions. Directionally dispersed distributions are shown to have a simple form for their density, which extends a spherically symmetric density function by including a function D modelling directional dispersion. Under a mild condition, the class of distributions is shown to preserve both unimodality and moment existence. By adequately defining D, it is possible to generate skewed distributions. Using spline models on hyperspheres, we suggest a very general, yet practical, implementation for modelling directional dispersion in any dimension. Finally, we use the new class of distributions in a Bayesian regression setup and analyse the distributions of a set of biomedical measurements and a sample of U.S. manufacturing firms.

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File URL: http://128.118.178.162/eps/em/papers/0410/0410006.pdf
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Bibliographic Info

Paper provided by EconWPA in its series Econometrics with number 0410006.

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Length: 17 pages
Date of creation: 18 Oct 2004
Date of revision:
Handle: RePEc:wpa:wuwpem:0410006

Note: Type of Document - pdf; pages: 17
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Web page: http://128.118.178.162

Related research

Keywords: Bayesian regression model; directional dispersion; elliptical distributions; existence of moments; modality; skewed distributions.;

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References

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  1. Steel, M.F.J., 1991. "Bayesian inference in time series," Discussion Paper 1991-53, Tilburg University, Center for Economic Research.
  2. J. T. A. S. Ferreira & M. F. J. Steel, 2004. "On Describing Multivariate Skewness: A Directional Approach," Econometrics 0409010, EconWPA.
  3. Jose T.A.S. Ferreira & Mark F.J. Steel, 2004. "Bayesian Multivariate Regression Analysis with a New Class of Skewed Distributions," Econometrics 0403001, EconWPA.
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Cited by:
  1. José T.A.S. Ferreira & Miguel A Juárez & MArk F.J. Steel, 2005. "Directional Log-spline Distributions," Econometrics 0511001, EconWPA.

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