The Multivariate Normal Distribution - Y. L. Tong

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Sommaire:
1 Introduction.- 1.1. Some Fundamental Properties.- 1.2. Historical Remarks.- 1.3. Characterization.- 1.4. Scope and Organization.- 2 The Bivariate Normal Distribution.- 2.1. Some Distribution Properties.- 2.2. The Distribution Function and Sampling Distributions.- 2.3. Dependence and the Correlation Coefficient.- Problems.- 3 Fundamental Properties and Sampling Distributions of the Multivariate Normal Distribution.- 3.1. Preliminaries.- 3.2. Definitions of the Multivariate Normal Distribution.- 3.3. Basic Distribution Properties.- 3.4. Regression and Correlation.- 3.5. Sampling Distributions.- Problems.- 4 Other Related Properties.- 4.1. The Elliptically Contoured Family of Distributions and the Multivariate Normal.- 4.2. Log-Concavity and Unimodality Properties.- 4.3. MTP2 and MRR2 Properties.- 4.4. Schur-Concavity Property.- 4.5. Arrangement-Increasing Property.- Problems.- 5 Positively Dependent and Exchangeable Normal Variables.- 5.1. Positively Dependent Normal Variables.- 5.2. Permutation-Symmetric Normal Variables.- 5.3. Exchangeable Normal Variables.- Problems.- 6 Order Statistics of Normal Variables.- 6.1. Order Statistics of Exchangeable Normal Variables.- 6.2. Positive Dependence of Order Statistics of Normal Variables.- 6.3. Distributions of Certain Partial Sums and Linear Combinations of Order Statistics.- 6.4. Miscellaneous Results.- Problems.- 7 Related Inequalities.- 7.1. Introduction.- 7.2. Dependence-Related Inequalities.- 7.3. Dimension-Related Inequalities.- 7.4. Probability Inequalities for Asymmetric Geometric Regions.- 7.5. Other Related Inequalities.- Problems.- 8 Statistical Computing Related to the Multivariate Normal Distribution.- 8.1. Generation of Multivariate Normal Variates.- 8.2. Evaluation and Approximations of Multivariate Normal Probability Integrals.- 8.3. Computation of One-Sided and Two-Sided Multivariate Normal Probability Integrals.- 8.4. The Tables.- Problems.- 9 The Multivariate t Distribution.- 9.1. Distribution Properties.- 9.2. Probability Inequalities.- 9.3. Convergence to the Multivariate Normal Distribution.- 9.4. Tables for Exchangeable t Variables.- Problems.- References.- Appendix-Tables.- Author Index.