Ingram Olkin

Written by renowned experts in the field, this reissue of a textbook has as its unifying theme the role that probability models have had, and continue to have, in scientific and practical applications. It includes many examples, with actual data, of real-world use of probability models, while expositing the mathematical theory of probability at an introductory calculus-based level. Detailed descriptions of the properties and applications of probability models that have successfully modeled real phenomena are given, as well as an explanation of methods for testing goodness of fit of these models. Readers will receive a firm foundation in techniques for deriving distributions of various summaries of data that will prepare them for subsequent studies of statistics, as well as a solid grounding in concepts such as that of conditional probability that will prepare them for more advanced courses in stochastic processes.

Written by renowned experts in the field, this reissue of a textbook has as its unifying theme the role that probability models have had, and continue to have, in scientific and practical applications. It includes many examples, with actual data, of real-world use of probability models, while expositing the mathematical theory of probability at an introductory calculus-based level. Detailed descriptions of the properties and applications of probability models that have successfully modeled real phenomena are given, as well as an explanation of methods for testing goodness of fit of these models. Readers will receive a firm foundation in techniques for deriving distributions of various summaries of data that will prepare them for subsequent studies of statistics, as well as a solid grounding in concepts such as that of conditional probability that will prepare them for more advanced courses in stochastic processes.

This book’s first edition has been widely cited by researchers in diverse fields. The following are excerpts from reviews. “Inequalities: Theory of Majorization and its Applications” merits strong praise. It is innovative, coherent, well written and, most importantly, a pleasure to read. … This work is a valuable resource!” (Mathematical Reviews). “The authors … present an extremely rich collection of inequalities in a remarkably coherent and unified approach. The book is a major work on inequalities, rich in content and original in organization.” (Siam Review). “The appearance of … Inequalities in 1979 had a great impact on the mathematical sciences. By showing how a single concept unified a staggering amount of material from widely diverse disciplines–probability, geometry, statistics, operations research, etc.–this work was a revelation to those of us who had been trying to make sense of his own corner of this material.” (Linear Algebra and its Applications). This greatly expanded new edition includes recent research on stochastic, multivariate and group majorization, Lorenz order, and applications in physics and chemistry, in economics and political science, in matrix inequalities, and in probability and statistics. The reference list has almost doubled.

This book’s first edition has been widely cited by researchers in diverse fields. The following are excerpts from reviews. “Inequalities: Theory of Majorization and its Applications” merits strong praise. It is innovative, coherent, well written and, most importantly, a pleasure to read. … This work is a valuable resource!” (Mathematical Reviews). “The authors … present an extremely rich collection of inequalities in a remarkably coherent and unified approach. The book is a major work on inequalities, rich in content and original in organization.” (Siam Review). “The appearance of … Inequalities in 1979 had a great impact on the mathematical sciences. By showing how a single concept unified a staggering amount of material from widely diverse disciplines–probability, geometry, statistics, operations research, etc.–this work was a revelation to those of us who had been trying to make sense of his own corner of this material.” (Linear Algebra and its Applications). This greatly expanded new edition includes recent research on stochastic, multivariate and group majorization, Lorenz order, and applications in physics and chemistry, in economics and political science, in matrix inequalities, and in probability and statistics. The reference list has almost doubled.

For over 200 years, practitioners have been developing parametric families of probability distributions for data analysis. More recently, an active development of nonparametric and semiparametric families has occurred. This book includes an extensive discussion of a wide variety of distribution families—nonparametric, semiparametric and parametric—some well known and some not. An all-encompassing view is taken for the purpose of identifying relationships, origins and structures of the various families. A unified methodological approach for the introduction of parameters into families is developed, and the properties that the parameters imbue a distribution are clarified. These results provide essential tools for intelligent choice of models for data analysis. Many of the results given are new and have not previously appeared in print. This book provides a comprehensive reference for anyone working with nonnegative data.

For over 200 years, practitioners have been developing parametric families of probability distributions for data analysis. More recently, an active development of nonparametric and semiparametric families has occurred. This book includes an extensive discussion of a wide variety of distribution families—nonparametric, semiparametric and parametric—some well known and some not. An all-encompassing view is taken for the purpose of identifying relationships, origins and structures of the various families. A unified methodological approach for the introduction of parameters into families is developed, and the properties that the parameters imbue a distribution are clarified. These results provide essential tools for intelligent choice of models for data analysis. Many of the results given are new and have not previously appeared in print. This book provides a comprehensive reference for anyone working with nonnegative data.

This SIAM Classics edition is an unabridged, corrected republication of the work first published in 1977. It provides a compendium of applied aspects of ordering and selection procedures and includes tables that permit the practitioner to carry out the experiment and draw statistically justified conclusions. These tables are not readily available in other texts. Although more than 1000 papers and several books on the general theory of ranking and selection have been published since this book first appeared, the methodology is presented in a more elementary fashion, with numerous examples to help the reader apply it to a specific problem.

The main purpose of this book is to address the statistical issues for integrating independent studies. There exist a number of papers and books that discuss the mechanics of collecting, coding, and preparing data for a meta-analysis , and we do not deal with these. Because this book concerns methodology, the content necessarily is statistical, and at times mathematical. In order to make the material accessible to a wider audience, we have not provided proofs in the text. Where proofs are given, they are placed as commentary at the end of a chapter. These can be omitted at the discretion of the reader. Throughout the book we describe computational procedures whenever required. Many computations can be completed on a hand calculator, whereas some require the use of a standard statistical package such as SAS, SPSS, or BMD. Readers with experience using a statistical package or who conduct analyses such as multiple regression or analysis of variance should be able to carry out the analyses described with the aid of a statistical package.