Premium
Modelling directional dispersion through hyperspherical log‐splines
Author(s) -
Ferreira José T. A. S.,
Steel Mark F. J.
Publication year - 2005
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/j.1467-9868.2005.00518.x
Subject(s) - unimodality , dispersion (optics) , mathematics , generalization , probability density function , spline (mechanical) , multivariate normal distribution , statistical physics , multivariate statistics , mathematical analysis , statistics , physics , optics , thermodynamics
Summary. We introduce the directionally dispersed class of multivariate distributions, a generalization 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 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 flexible, yet practical, implementation for modelling directional dispersion in any dimension. Finally, we use the new class of distributions in a Bayesian regression set‐up and analyse the distributions of a set of biomedical measurements and a sample of US manufacturing firms.