The Multivariate Normal Distribution
Published in December 1989
Book
Hardback
XIII, 271 pages
978-3-540-97062-0 (ISBN)
Description
This text represents a comprehensive treatment of the results related to the multivariate normal distribution. In addition to the classical topics on distribution theory, correlation analysis and sampling distributions, it also contains recent results reported in relevant literature. The material is organized in a unified modern approach, and the main themes are dependence, probability inequalities, and their roles in theory and applications. Some of the properties (such as log-concavity, unimodality, Schurconcavity and total positivity) of a multivariate normal density function are discussed, and results that follow from these properties and reviewed. The volume also includes tables of the equi-coordinate percentage points and probability inequalities for exchangeable normal variables. The volume should be accessible to graduate students and advanced undergraduates in statistics, mathematics, and related applied areas, and can be used as a reference in a course on multivariate analysis.
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Content
Contents: Introduction.- The Bivariate Normal Distribution.- Fundamental Properties and Sampling Distributions of the Multivariate Normal Distribution.- Other Related Properties.- Positively Dependent and Exchangeable Normal Variables.- Order Statistics of Normal Variables.- Related Inequalities.- Statistical Computing Related to the Multivariate Normal Distribution.- The Multivariate t Distribution.- References.- Appendix.- Tables.- Author Index.- Subject Index.