Gaussian Approximation to the Joint Distributions of Definite Quadratic Forms.
Abstract
*Sampling, *Distribution functions, *Approximation, Matrices(Mathematics), Statistical tests, Multivariate analysis, Transformations(Mathematics), TheoremsQuadratic forms, Central limit theoremPower transformations of the Wilson-Hilferty type are developed to provide multidimensional Gaussian approximations to the joint distributions of definite quadratic forms in Gaussian variables. Numerous applications are cited. The parameters of the approximating Gaussian distribution are given up to terms of order O(nu sup (-3)) in the degrees of freedom nu. These expressions simplify considerably in some special cases of practical importance. The accuracy of the approximation is studied numerically in a variety of cases for which exact probabilities can be found, and the evidence suggests the approximation to be satisfactory over a wide range of the parameters. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 15, 1973
- Accession Number
- AD0771720
Entities
People
- Donald R. Jensen
Organizations
- Virginia Tech