Multivariate Statistical Simulation

Provides state-of-the-art coverage for the researcher confronted with designing and executing a simulation study using continuous multivariate distributions. Concise writing style makes the book accessible to a wide audience. Well-known multivariate distributions are described, emphasizing a few representative cases from each distribution. Coverage includes Pearson Types II and VII elliptically contoured distributions, Khintchine distributions, and the unifying class for the Burr, Pareto, and logistic distributions. Extensively illustrated--the figures are unique, attractive, and reveal very nicely what distributions ``look like.'' Contains an extensive and up-to-date bibliography culled from journals in statistics, operations research, mathematics, and computer science.

1;Cover;1 2;Title Page;5 3;Copyright Page;6 4;Preface;7 5;Contents;9 6;1. Introduction;13 6.1;1.1. Robustness of Hotelling's T2 Statistic;16 6.2;1.2. Error Rates in Partial Discriminant Analysis;18 6.3;1.3. Foutz' Test;23 6.4;1.4. Overview;27 7;2. Univariate Distributions and their Generation;30 7.1;2.1. General Methods for Continuous Univariate Generation;31 7.2;2.2. Normal Generators;41 7.3;2.3. Johnson's Translation System;43 7.4;2.4. Generalized Exponential Power Distribution;46 7.5;2.5. Gamma Generators;50 7.6;2.6. Uniform 01 Generators;53 8;3. Multivariate Generation Techniques;55 8.1;3.1. Conditional Distribution Approach;55 8.2;3.2. Transformation Approach;57 8.3;3.3. Rejection Approach;58 9;4. Multivariate Normal and Related Distributions;61 9.1;4.1. Multivariate Normal Distribution;61 9.2;4.2. Mixtures of Normal Variates;67 10;5. Johnson's Translation System;75 10.1;5.1. Plots for the SLL Distribution;77 10.2;5.2. Plots for the SUU Distribution;82 10.3;5.3. Contour Plots for the SBB Distribution;88 10.4;5.4. Analytical Results;95 10.5;5.5. Discriminant Analysis Applications;111 11;6. Elliptically Contoured Distributions;118 11.1;6.1. General Results for Elliptically Contoured Distributions;118 11.2;6.2. Special Cases of Elliptically Contoured Distributions;122 12;7. Circular, Spherical, and Related Distributions;137 12.1;7.1. Uniform Distributions;137 12.2;7.2. Nonuniform Distributions;147 13;8. Khintchine Distributions;161 13.1;8.1. Khintchine's Unimodality Theorem;161 13.2;8.2. Identical Generators;164 13.3;8.3. Independent Generators;165 13.4;8.4. Other Possibilities;166 14;9. Multivariate Burr, Pareto, and Logistic Distributions;172 14.1;9.1. Standard Form and Properties;172 14.2;9.2. Generalizations;182 15;10. Miscellaneous Distributions;192 15.1;10.1. Morgenstern's Distribution;192 15.2;10.2. Plackett's Distribution;203 15.3;10.3. Gumbel's Bivariate Exponential Distribution;209 15.4;10.4. Ali-Mikhail-Haq's Distribution;211 15.5;10.5. Wishart Distribu
tion;215 16;11. Research Directions;217 17;References;223 18;Supplementary References;231 19;Author Index;237 20;Subject Index;241