Multivariate Bonferroni-Type Inequalities: Theory and Applications presents a systematic account of research discoveries on multivariate Bonferroni-type inequalities published in the past decade. The emergence of new bounding approaches pushes the conventional definitions of optimal inequalities and demands new insights into linear and Fréchet optimality. The book explores these advances in bounding techniques with corresponding innovative applications. It presents the method of linear programming for multivariate bounds, multivariate hybrid bounds, sub-Markovian bounds, and bounds using Hamilton circuits. The first half of the book describes basic concepts and methods in probability inequalities. The author introduces the classification of univariate and multivariate bounds with optimality, discusses multivariate bounds using indicator functions, and explores linear programming for bivariate upper and lower bounds. The second half addresses bounding results and applications of multivariate Bonferroni-type inequalities. The book shows how to construct new multiple testing procedures with probability upper bounds and goes beyond bivariate upper bounds by considering vectorized upper and hybrid bounds. It presents an optimization algorithm for bivariate and multivariate lower bounds and covers vectorized high-dimensional lower bounds with refinements, such as Hamilton-type circuits and sub-Markovian events. The book concludes with applications of probability inequalities in molecular cancer therapy, big data analysis, and more.

Bonferroni-Type Inequalities with Applications presents a large variety of extensions of the methods of inclusion and exclusion. Both methods for generating and methods for proof of such inequalities are discussed. The inequalities are utilized for finding classical probability estimates to modern extreme value theory and combinatorial counting to random subset selection. Applications are given in prime number theory, growth of digits in different algorithms, and in statistics such as estimates of confidence levels of simultaneous interval estimation. The prerequisites include the basic concepts of probability theory and familiarity with combinatorial arguments.

Aims to provide in-depth descriptions of the latest developments in multiple comparison methods and selection procedures, while emphasizing biometry. This text is published in honour of the 70th birthday of Charles W. Dunnett - a pioneer in statistical methodology.

Professor Herbert A. David of Iowa State University will be turning 70 on December 19, 1995. He is reaching this milestone in life with a very distinguished career as a statistician, educator and administrator. We are bringing out this volume in his honor to celebrate this occasion and to recognize his contributions to order statistics, biostatistics and design of experiments, among others; and to the statistical profession in general. With great admiration, respect and pleasure we dedicate this festschrift to Professor Herbert A. David, also known as Herb and H.A. among his friends, colleagues and students. When we began this project in Autumn 1993 and contacted potential contributors from the above group, the enthu siasm was phenomenal. The culmination of this collective endeavor is this volume that is being dedicated to him to celebrate his upcoming birthday. Several individuals have contributed in various capacities to the success ful completion of this project. We sincerely thank the authors of the papers appearing here. Without their dedicated work, we would just have this pref ace! Many of them have served as (anonymous) referees as well. In addition, we are thankful to the following colleagues for their time and advice: John Bunge (Cornell), Z. Govindarajulu (Kentucky), John Klein (Medical U.

Upon publication, the first edition of the CRC Concise Encyclopedia of Mathematics received overwhelming accolades for its unparalleled scope, readability, and utility. It soon took its place among the top selling books in the history of Chapman & Hall/CRC, and its popularity continues unabated. Yet also unabated has been the d

This volume contains twenty-two original contributions by leading scientists in many important areas of probability theory and its applications. The material also includes significant new results. Together this collection of papers provides a good state-of-the-art survey of current research in the following areas: inequalities; limit theorems; renewal theory and reliability theory; characterizations of distributions; infinite divisibility of polynomials of normal variables; limiting distributions for order statistics; stochastic processes; functional equations in engineering model building; and probabilistic number theory.

The study of scan statistics and their applications to many different scientific and engineering problems have received considerable attention in the literature recently. In addition to challenging theoretical problems, the area of scan statis tics has also found exciting applications in diverse disciplines such as archaeol ogy, astronomy, epidemiology, geography, material science, molecular biology, reconnaissance, reliability and quality control, sociology, and telecommunica tion. This will be clearly evident when one goes through this volume. In this volume, we have brought together a collection of experts working in this area of research in order to review some of the developments that have taken place over the years and also to present their new works and point out some open problems. With this in mind, we selected authors for this volume with some having theoretical interests and others being primarily concerned with applications of scan statistics. Our sincere hope is that this volume will thus provide a comprehensive survey of all the developments in this area of research and hence will serve as a valuable source as well as reference for theoreticians and applied researchers. Graduate students interested in this area will find this volume to be particularly useful as it points out many open challenging problems that they could pursue. This volume will also be appropriate for teaching a graduate-level special course on this topic.

The first and only book to make this research available in the West Concise and accessible: proofs and other technical matters are kept to a minimum to help the non-specialist Each chapter is self-contained to make the book easy-to-use

This monograph of carefully collected articles reviews recent developments in theoretical and applied statistical science, highlights current noteworthy results and illustrates their applications; and points out possible new directions to pursue. With its enlightening account of statistical discoveries and its numerous figures and tables, Probabili

The study of measurement and statistics can be less than inviting. However, in fields as varying as education, politics, and health care, assessment and the use of measurement and statistics have become integral parts of almost every activity undertaken. These activities require the organization of ideas, the generation of hypotheses, the collection of data, and the interpretation, illustration, and analysis of data. No matter where educated people look, this critical analysis is more important than ever in an age where information—and lots of it—is readily available. The ideas and tools contained in the Encyclopedia of Measurement and Statistics are approachable and can be invaluable for understanding a very technical world and the increasing flow of information. Although there are references that cover statistics and assessment in depth, none provides as comprehensive a resource in as focused and accessible a manner as the three volumes of this Encyclopedia. Through approximately 500 contributions, experts provide an overview and an explanation of the major topics in these two areas. Key Features Covers every major facet of these two different, but highly integrated disciplines—from mean, mode, and median to reliability, validity, significance, correlation, and much more—all without overwhelming the informed reader Offers cross-disciplinary coverage, with contributions from and applications to the fields of Psychology, Education, Sociology, Human Development, Political Science, Business and Management, Public Health, and others Provides cross-reference terms, further readings, and Web site URLs following most entries, as well as an extensive set of appendices and an annotated list of organizations relevant to measurement and statistics Appendices Features Appendix A is a guide to basic statistics for those readers who might like an instructional step-by-step presentation of basic concepts in statistics and measurement Appendix B is a table of critical values used in hypothesis testing and an important part of any reference in this area Appendix C represents a collection of some important and useful measurement and statistics Internet sites A primary goal of creating this set of volumes is to open up the broad discipline of measurement and statistics to a wider and more general audience than usual. Edited by bestselling author Neil J. Salkind, this Encyclopedia is specifically designed to appeal to beginning and intermediate-level students, practitioners, researchers, and consumers of information. It is a welcome addition to any academic library.