ON THE DISTRIBUTION OF QUADRATIC FORMS

Abstract

A study is made of definite quadratic forms in both central and noncentral independent normal variates, and an application is given for each distribution. Two special cases of an indefinite quadratic form are discussed: the distribution of the difference between 2 independent chi-squares with different numbers of degrees of freedom, and the probability density function of an indefinite quadratic form when the latent roots of the matrix of the form are equal in pairs. Some inequalities are included for the distribution of a quadratic form in independent identically distributed variates, each of which is central normal or more general.

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Document Details

Document Type
Technical Report
Publication Date
Jul 15, 1953
Accession Number
AD0018066

Entities

People

  • James Pachares

Organizations

  • University of North Carolina at Chapel Hill

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Analysis Of Variance
  • Bessel Functions
  • Data Science
  • Dirichlet Integral
  • Distribution Functions
  • Errors
  • Inequalities
  • Information Science
  • Integrals
  • Normal Distribution
  • Numerical Quadrature
  • Observation
  • Probability
  • Probability Density Functions
  • Random Variables
  • Statistics

Fields of Study

  • Mathematics

Readers

  • Statistical inference.