The Multivariate Normal Distribution

This book represents a comprehensive and coherent 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 important results reported recently in the literature, but which cannot be found in most books on multivariate analysis. 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 extensively. The volume also includes tables of the equi-coordinate percentage points and probability inequalities for exchangeable normal variables. The volume is 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.