Contributions to Probability and Statistics

Preface v.- I An Appreciation.- A Brief Biography and Appreciation of Ingram Olkin.- A Conversation with Ingram Olkin.- Bibliography of Ingram Olkin 35.- II Contributions to Probability and Statistics.- A Probability Inequalities and Characterizations.- 1 A Convolution Inequality.- 2 Peakedness of Weighted Averages of Jointly Distributed Random Variables.- 3 Multivariate Majorization.- 4 Some Results on Convolutions and a Statistical Application.- 5 The X + Y, X/Y Characterization of the Gamma Distribution.- 6 A Bivariate Uniform Distribution.- 7 Multinomial Problems in Geometric Probability with Dirichlet Analysis.- 8 Probability Inequalities for n-Dimensional Rectangles via Multivariate Majorization.- 9 Minimum Majorization Decomposition.- B Multivariate Analysis and Association.- 10 The Asymptotic Distribution of Characteristic Roots and Vectors in Multivariate Components of Variance.- 11 Univariate and Multivariate Analyses of Variance for Incomplete Factorial Experiments Having Monotoqp Structure in Treatments.- 12 The Limiting Distribution of the Rank Correlation Coefficient $${R_g}$$.- 13 Mean and Variance of Sample Size in Multivariate Heteroscedastic Method.- 14 A Comparative Study of Cluster Analysis and MANCOVA in the Analysis of Mathematics Achievement Data.- 15 Bayesian Inference in Factor Analysis.- 16 Computational Aspects of Association for Bivariate Discrete Distributions.- C Linear and Nonlinear Models, Ranking and Selection, Design.- 17 A Comparison of the Performances of Procedures for Selecting the Normal Population Having the Largest Mean when the Variances are Known and Equal.- 18 Parametric Empirical Bayes Rules for Selecting the Most Probable Multinomial Event.- 19 Bayesian Estimation in Two-Way Tables With Heterogeneous Variances.- 20 Calibrating For Differences.- 21 Complete Class Results For Linear Regression Designs Over The Multi-Dimensional Cube.- 22 A Unified Method of Estimation in Linear Models with Mixed Effects.- 23 Shrinking