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The Multivariate Normal Distribution

  • Textbook
  • © 1990

Overview

Authors:
  1. Y. L. Tong

    1. School of Mathematics, Georgia Institute of Technology, Atlanta, USA

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Part of the book series: Springer Series in Statistics (SSS)

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Introduction

    • Y. L. Tong
    Pages 1-5

  3. The Bivariate Normal Distribution

    • Y. L. Tong
    Pages 6-22

  4. Fundamental Properties and Sampling Distributions of the Multivariate Normal Distribution

    • Y. L. Tong
    Pages 23-61

  5. Other Related Properties

    • Y. L. Tong
    Pages 62-90

  6. Positively Dependent and Exchangeable Normal Variables

    • Y. L. Tong
    Pages 91-122

  7. Order Statistics of Normal Variables

    • Y. L. Tong
    Pages 123-149

  8. Related Inequalities

    • Y. L. Tong
    Pages 150-180

  9. Statistical Computing Related to the Multivariate Normal Distribution

    • Y. L. Tong
    Pages 181-201

  10. The Multivariate t Distribution

    • Y. L. Tong
    Pages 202-217

  11. Back Matter

    Pages 219-271
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Keywords

About this book

The multivariate normal distribution has played a predominant role in the historical development of statistical theory, and has made its appearance in various areas of applications. Although many of the results concerning the multivariate normal distribution are classical, there are important new results which have been reported recently in the literature but cannot be found in most books on multivariate analysis. These results are often obtained by showing that the multivariate normal density function belongs to certain large families of density functions. Thus, useful properties of such families immedi­ ately hold for the multivariate normal distribution. This book attempts to provide a comprehensive and coherent treatment of the classical and new results related to the multivariate normal distribution. The material is organized in a unified modern approach, and the main themes are dependence, probability inequalities, and their roles in theory and applica­ tions. Some general properties of a multivariate normal density function are discussed, and results that follow from these properties are reviewed exten­ sively. The coverage is, to some extent, a matter of taste and is not intended to be exhaustive, thus more attention is focused on a systematic presentation of results rather than on a complete listing of them.

Authors and Affiliations

  • School of Mathematics, Georgia Institute of Technology, Atlanta, USA

    Y. L. Tong

Bibliographic Information

  • Book Title: The Multivariate Normal Distribution

  • Authors: Y. L. Tong

  • Series Title: Springer Series in Statistics

  • DOI: https://doi.org/10.1007/978-1-4613-9655-0

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York Inc. 1990

  • Softcover ISBN: 978-1-4613-9657-4Published: 06 December 2011

  • eBook ISBN: 978-1-4613-9655-0Published: 06 December 2012

  • Series ISSN: 0172-7397

  • Series E-ISSN: 2197-568X

  • Edition Number: 1

  • Number of Pages: XIII, 271

  • Topics: Economic Theory/Quantitative Economics/Mathematical Methods

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