The probability content of cones in isotropic random fields
type: Item
instance of: scholarly article
title: The probability content of cones in isotropic random fields
zbMATH Open document ID: 0924.62049
author: Serge B. Provost
author: Young-Ho Cheong
published in: Journal of Multivariate Analysis
publication date: 1999-11-09T00:00:00Z
review text: Quadratic forms \(X'AX\), where \(X\) is a central elliptically contoured random vector and \(A\) is a symmetric matrix, are considered. Computable representations for the evaluation of the probability content of cones in isotropic random fields are given. A decomposition of quadratic forms in spherically symmetric random vectors is obtained and a simple representation of their moments is derived. These results allowed to obtain the distribution of quadratic forms in spherically symmetric or central elliptically contoured random vectors. Ratios of quadratic forms are also discussed.
Mathematics Subject Classification ID: 62H05
Mathematics Subject Classification ID: 62E15
Mathematics Subject Classification ID: 60G10
Mathematics Subject Classification ID: 62E10
zbMATH DE Number: 1211577
zbMATH Keywords: spherically symmetric distributions
zbMATH Keywords: elliptically contoured distributions
zbMATH Keywords: serial covariance
zbMATH Keywords: moments
zbMATH Keywords: cones
zbMATH Keywords: random fields
zbMATH Keywords: quadratic forms
reviewed by: Jarosław Bartoszewicz
MaRDI profile type: Publication
full work available at URL: jmva.1998.1750
OpenAlex ID: W2081102407
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DOI: 10.1006/JMVA.1998.1750
description: scientific article; zbMATH DE number 1211577