The Multivariate Normal Distribution

Description

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. Front Matter....Pages i-xiii Introduction....Pages 1-5 The Bivariate Normal Distribution....Pages 6-22 Fundamental Properties and Sampling Distributions of the Multivariate Normal Distribution....Pages 23-61 Other Related Properties....Pages 62-90 Positively Dependent and Exchangeable Normal Variables....Pages 91-122 Order Statistics of Normal Variables....Pages 123-149 Related Inequalities....Pages 150-180 Statistical Computing Related to the Multivariate Normal Distribution....Pages 181-201 The Multivariate t Distribution....Pages 202-217 Back Matter....Pages 219-271