The Intersection of Random Spheres and the Noncentral Radial Error Distribution for Spherical Models

Abstract

The paper gives an expression suitable for numerical computation and recursive relationships for the expected volume of the intersection of an $n$ dimensional sure sphere and an $n$ dimensional random sphere with a different radius, whose center follows a spherical distribution, the center of which does not coincide with that of the sure sphere. Several expressions are given for the distribution of the squared noncentral radial error when the vector observation follows a spherical distribution--a generalization of the noncentral chi-square distribution. Applications to specific spherical models are presented.