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

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Data Science
  • Distribution Functions
  • Gaussian Distributions
  • Information Science
  • Mathematical Analysis
  • Mathematics
  • Multivariate Analysis
  • Probability
  • Statistical Analysis
  • Statistical Tests
  • Statistics
  • Stochastic Processes

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Calculus or Mathematical Analysis