The Distribution of a Truncated Linear Difference between Independent Chi-Square Variates

Abstract

A comprehensive account is given of the properties of the distribution of a doubly-truncated linear difference between two independent chi-square variates. Expressions for the probability density function, distribution function, moments, moment generating function, and characteristic function of the distribution are obtained, primarily by making use of known results on hypergeometric functions. Emphasis is placed on representations thought to be useful for computations. In general, simple expressions are possible only when at least one of the chi-squares has an even number of degrees of freedom. The results should prove useful in studying the properties of truncated quadratic estimators of variance components.

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1971
Accession Number
AD0732287

Entities

People

  • David A. Harville

Organizations

  • Air Force Research Laboratory

Tags

Communities of Interest

  • Space

DTIC Thesaurus Topics

  • Accuracy
  • Air Force
  • Applied Mathematics
  • Computations
  • Data Science
  • Department Of Defense
  • Distribution Functions
  • Errors
  • Estimators
  • Hypergeometric Functions
  • Information Science
  • Mathematics
  • Probability
  • Probability Density Functions
  • Probability Distributions
  • Random Variables
  • Truncation

Fields of Study

  • Mathematics

Readers

  • Statistical inference.