Distribution of functionals of a Ferguson–Dirichlet process over an -dimensional ball (original) (raw)

On the characterization of spherical distributions

Journal of Information and Optimization Sciences, 1996

A necessary and sufficient condition has been derived for a random variable to have a spherical distribution. This result has been specialized to find characteristic functions of uniform distributions on or inside unit hyperspheres.

Uniform Distributions on Spheres in Finite DimensionalLαand Their Generalizations

Journal of Multivariate Analysis, 1998

We characterize uniform distributions on spheres in n-dimensional spaces L : by certain Cauchy-like (n&1)-dimensional distributions of the quotients and derive some properties of mixtures of uniform distributions on such spheres, i.e., :-spherical distributions. We feel that a simple Cauchy-like distribution is much simpler to deal with than the usual description of a uniform distribution on the sphere.

Uniform Distributions on Generalized Spheres in Finite Dimensional Spaces

We characterize uniform distributions on spheres in n-dimensional spaces L : by certain Cauchy-like (n&1)-dimensional distributions of the quotients and derive some properties of mixtures of uniform distributions on such spheres, i.e., :-spherical distributions. We feel that a simple Cauchy-like distribution is much simpler to deal with than the usual description of a uniform distribution on the sphere.

Generalized Dirichlet distributions on the ball and moments

2010

The geometry of unit NNN-dimensional ellp\ell_{p}ellp balls has been intensively investigated in the past decades. A particular topic of interest has been the study of the asymptotics of their projections. Apart from their intrinsic interest, such questions have applications in several probabilistic and geometric contexts (Barthe et al. 2005). In this paper, our aim is to revisit some known results of this flavour with a new point of view. Roughly speaking, we will endow the ball with some kind of Dirichlet distribution that generalizes the uniform one and will follow the method developed in Skibinsky (1967), Chang et al. (1993) in the context of the randomized moment space. The main idea is to build a suitable coordinate change involving independent random variables. Moreover, we will shed light on a nice connection between the randomized balls and the randomized moment space.