Theory and Applications of Elliptically Contoured and Related Distributions

Abstract

A random vector X is said to have elliptically contoured distribution if it has the distribution of micron + AY, where micron is a constant matrix, and the random vector Y has a spherical distributed; that is, Y is distributed as QY for every orthogonal matrix Q. This paper surveys recent work on distribution theory and statistical inference for elliptically contoured distributions. It emphasizes the contributions of the authors and of the students and associates of the second author; it gives a picture of this area of multivariate analysis that is particularly active in the People's Republic of China. Included are classifications of elliptically contoured and related distributions, distributions of quadratic forms, estimation of parameters, testing hypotheses, and applications. Since the normal distribution is in the class, the properties of elliptically contoured distributions are similar to those of the normal distribution.

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1990
Accession Number
ADA230672

Entities

People

  • Kai-tai Fang
  • Theodore W. Anderson

Organizations

  • Stanford University

Tags

Communities of Interest

  • Energy and Power Technologies
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Correlation Analysis
  • Data Mining
  • Data Science
  • Distribution Theory
  • Factor Analysis
  • Information Science
  • Military Research
  • Multivariate Analysis
  • Normal Distribution
  • Order Statistics
  • Probability
  • Random Variables
  • Regression Analysis
  • Statistical Algorithms
  • Statistical Analysis
  • Statistical Inference
  • Surveys

Fields of Study

  • Mathematics

Readers

  • Statistical inference.
  • Theoretical Analysis.

Technology Areas

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