On the Exact Distributions of the Test Statistics Based on the Eigenvalues of Complex Random Matrices

Abstract

In the report, the author considers the derivation of the exact noncentral distributions of certain test statistics based upon the eigenvalues of a class of complex random matrices. This class of random matrices include Wishart matrix, MANOVA matrix, canonical correlation matrix and the two-sample covariance model matrix in the complex case. The moments of the elementary symmetric functions as well as the Laplace transformations of the traces of the above class of random matrices are derived. Also, the exact distributions of any few roots as well as the distributions of certain ratios of the roots of the above class of random matrices are derived. In addition, the exact noncentral distribution of the trace of the complex MANOVA matrix is derived.

Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1973
Accession Number
AD0776315

Entities

People

  • Paruchuri R. Krishnaiah

Organizations

  • Air Force Research Laboratory

Tags

Communities of Interest

  • Space

DTIC Thesaurus Topics

  • Air Force
  • Air Force Facilities
  • Covariance
  • Data Science
  • Distribution Functions
  • Eigenvalues
  • Gaussian Distributions
  • Government Procurement
  • Governments
  • Information Science
  • Integrals
  • Laplace Transformation
  • Multivariate Analysis
  • Normal Distribution
  • Statistical Analysis
  • Statistics
  • Wishart Matrices

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Regression Analysis.