Author | Tong, Y. L. author |
---|---|
Title | The Multivariate Normal Distribution [electronic resource] / by Y. L. Tong |
Imprint | New York, NY : Springer New York, 1990 |
Connect to | http://dx.doi.org/10.1007/978-1-4613-9655-0 |
Descript | XIII, 271 p. online resource |
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 -- AppendixโTables -- Author Index