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January, 1974 The Intersection of Random Spheres and the Noncentral Radial Error Distribution for Spherical Models
Andre G. Laurent
Ann. Statist. 2(1): 182-189 (January, 1974). DOI: 10.1214/aos/1176342624

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.

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Andre G. Laurent. "The Intersection of Random Spheres and the Noncentral Radial Error Distribution for Spherical Models." Ann. Statist. 2 (1) 182 - 189, January, 1974. https://doi.org/10.1214/aos/1176342624

Information

Published: January, 1974
First available in Project Euclid: 12 April 2007

zbMATH: 0273.62037
MathSciNet: MR353567
Digital Object Identifier: 10.1214/aos/1176342624

Subjects:
Primary: 62H10
Secondary: 44A30 , 60D05

Keywords: multivariate transforms , noncentral radial error , random sets , spherical distributions

Rights: Copyright © 1974 Institute of Mathematical Statistics

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Vol.2 • No. 1 • January, 1974
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