Matrix Variate Distributions: 1st Edition (Hardback) book cover

Matrix Variate Distributions

1st Edition

By A K Gupta, D K Nagar

Chapman and Hall/CRC

384 pages

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Hardback: 9781584880462
pub: 1999-10-22
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Description

Useful in physics, economics, psychology, and other fields, random matrices play an important role in the study of multivariate statistical methods. Until now, however, most of the material on random matrices could only be found scattered in various statistical journals. Matrix Variate Distributions gathers and systematically presents most of the recent developments in continuous matrix variate distribution theory and includes new results.

After a review of the essential background material, the authors investigate the range of matrix variate distributions, including:

  • matrix variate normal distribution

  • Wishart distribution

  • Matrix variate t-distribution

  • Matrix variate beta distribution

  • F-distribution

  • Matrix variate Dirichlet distribution

  • Matrix quadratic forms

    With its inclusion of new results, Matrix Variate Distributions promises to stimulate further research and help advance the field of multivariate statistical analysis.

  • Reviews

    "This book is about probability distributions for random matrices."

    Biometrics, Vol. 56, No. 3, September 2000

    "I am sure that the book will be welcomed by specialists, because of its systematic and thorough coverage of the different distributions."

    Biometrics, Vol. 56, No. 3, September 2000

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    Table of Contents

    PRELIMINARIES

    Matrix Algebra

    Jacobians of Transformations

    Integration

    Zonal Polynomials

    Hypergeometric Functions of Matrix Argument

    LaGuerre Polynomials

    Generalized Hermite Polynomials

    Notion of Random Matrix Problems

    MATRIX VARIATE NORMAL DISTRIBUTION

    Density Function

    Properties

    Singular Matrix Variate Normal distribution

    Symmetic Matrix Variate Normal Distribution

    Restricted Matrix Variate Normal Distribution

    Matrix Variate Q-Generalized Normal Distribution

    WISHART DISTRIBUTION

    Introduction

    Density Function

    Properties

    Inverted Wishart Distribution

    Noncentral Wishart Distribution

    Matrix Variate Gamma Distribution

    Approximations

    MATRIX VARIATE t-DISTRIBUTION

    Density Function

    Properties

    Inverted Matrix Variate t-Distribution

    Disguised Matrix Variate t-Distribution

    Restricted Matrix Variate t-Distribution

    Noncentral Matrix Variate t-Distribution

    Distribution of Quadratic Forms

    MATRIX VARIATE BETA DISTRIBUTIONS

    Density Functions

    Properties

    Related Distributions

    Noncentral Matrix Variate Beta Distribution

    MATRIX VARIATE DIRICHLET DISTRIBUTIONS

    Density Functions

    Properties

    Related Distributions

    Noncentral Matrix Variate Dirichlet Distributions

    DISTRIBUTION OF MATRIX QUADRATIC FORMS

    Density Function

    Properties

    Functions of Quadratic Forms

    Series Representation of the Density

    Noncentral Density Function

    Expected Values

    Wishartness and Independence of Quadratic Forms of the Type XAX'

    Wishartness and Independence of Quadratic Forms of the Type XAX'+1/2(LX'+XL')+C

    Wishartness and Independence of Quadratic Forms of the Type XAX'+L1X'+XL'2+C

    MISCELLANEOUS DISTRIBUTIONS

    Uniform Distribution on Stiefel Manifold

    Von Mises-Fisher Distribution

    Bingham Matrix Distribution

    Generalized Bingham-Von Mises Matrix Distribution

    Manifold Normal Distribution

    Matrix Angular Central Gaussian Distribution

    Bimatix Wishart Distribution

    Beta-Wishart Distribution

    Confluent Hypergeometric Function Kind 1 Distribution

    Confluent Hypergeometric Function Kind 2 Distribution

    Hypergeometric Function Distributions

    Generalized Hypergeometric Function Distributions

    Complex Matrix Variate Distributions

    GENERAL FAMILIES OF MATRIX VARIATE DISTRIBUTIONS

    Matrix Variate Liouville Distributions

    Matrix Variate Spherical Distributions

    Matrix Variate Elliptically Contoured Distributions

    Orthogonally Invariant and Residual Independent Matrix Distributions

    GLOSSARY

    REFERENCES

    SUBJECT INDEX

    Each chapter also includes an Introduction and Problems

    @

    About the Series

    Monographs and Surveys in Pure and Applied Mathematics

    Learn more…

    Subject Categories

    BISAC Subject Codes/Headings:
    MAT003000
    MATHEMATICS / Applied
    MAT029000
    MATHEMATICS / Probability & Statistics / General