A Disguised Wishart Variable and a Related Theorem.

Abstract

In considering the construction of a tolerance region of beta-expectation from the Bayesian point of view, the authors were confronted with finding the distribution of the (kxk) matrix of random variables R = P'VP, where PP' = (Sigma sup -1), and where the (kxk) matrix (Sigma sup -1) has the Wishart distribution, matrix ((n-1)V) sup-1, and degrees of freedom (n-1), with V a symmetric kxk positive definite matrix of constants. In the paper, the authors find this distribution for the case where P is a lower triangular matrix with positive diagonal elements. (Author)

Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1971
Accession Number
AD0739440

Entities

People

  • Irwin Guttman
  • W. Y. Tan

Organizations

  • University of Wisconsin–Madison

Tags

DTIC Thesaurus Topics

  • Construction
  • Mathematics
  • Random Variables

Readers

  • Linear Algebra
  • Regression Analysis.

Technology Areas

  • AI & ML
  • AI & ML - Bayesian Inference
  • AI & ML - Machine Learning Algorithms