The probability content of cones in isotropic random fields
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.
scientific article; zbMATH DE number 1211577
scientific article