Modelling Directional Dispersion Through Hyperspherical Log- Splines
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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- Steel, M.F.J., 1991.
"Bayesian Inference in Time Series,"
9153, Tilburg - Center for Economic Research.
- Jose T.A.S. Ferreira & Mark F.J. Steel, 2004. "Bayesian Multivariate Regression Analysis with a New Class of Skewed Distributions," Econometrics 0403001, EconWPA.
- J. T. A. S. Ferreira & M. F. J. Steel, 2004. "On Describing Multivariate Skewness: A Directional Approach," Econometrics 0409010, EconWPA.
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