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Advances in Statistics - Theory and Applications
This edited collection brings together internationally recognized experts in a range of areas of statistical science to honor the contributions of the distinguished statistician, Barry C. Arnold. A pioneering scholar and professor of statistics at the University of California, Riverside, Dr. Arnold has made exceptional advancements in different areas of probability, statistics, and biostatistics, especially in the areas of distribution theory, order statistics, and statistical inference. As a tribute to his work, this book presents novel developments in the field, as well as practical applications and potential future directions in research and industry. It will be of interest to graduate students and researchers in probability, statistics, and biostatistics, as well as practitioners and technicians in the social sciences, economics, engineering, and medical sciences.
Pareto Distributions
Since the publication of the first edition over 30 years ago, the literature related to Pareto distributions has flourished to encompass computer-based inference methods. Pareto Distributions, Second Edition provides broad, up-to-date coverage of the Pareto model and its extensions. This edition expands several chapters to accommodate recent result
A First Course in Order Statistics
This updated classic text will aid readers in understanding much of the current literature on order statistics: a flourishing field of study that is essential for any practising statistician and a vital part of the training for students in statistics. Written in a simple style that requires no advanced mathematical or statistical background, the book introduces the general theory of order statistics and their applications. The book covers topics such as distribution theory for order statistics from continuous and discrete populations, moment relations, bounds and approximations, order statistics in statistical inference and characterisation results, and basic asymptotic theory. There is also a short introduction to record values and related statistics. The authors have updated the text with suggestions for further reading that may be used for self-study. Written for advanced undergraduate and graduate students in statistics and mathematics, practising statisticians, engineers, climatologists, economists, and biologists.
Majorization and the Lorenz Order: A Brief Introduction
My interest in majorization was first spurred by Ingram aIkin's proclivity for finding Schur convex functions lurking in the problem section of every issue of the American Mathematical Monthly. Later my interest in income inequality led me again to try and "really" understand Hardy, Littlewood and Polya' s contributions to the majori zation literature. I have found the income distribution context to be quite convenient for discussion of inequality orderings. The pre sent set of notes is designed for a one quarter course introducing majorization and the Lorenz order. The inequality principles of Dalton, especially the transfer or Robin Hood principle, are given appropriate prominence. Initial...
Advances in Statistics -- Theory and Applications
This edited collection brings together internationally recognized experts in a range of areas of statistical science to honor the contributions of the distinguished statistician, Barry C. Arnold. A pioneering scholar and professor of statistics at the University of California, Riverside, Dr. Arnold has made exceptional advancements in different areas of probability, statistics, and biostatistics, especially in the areas of distribution theory, order statistics, and statistical inference. As a tribute to his work, this book presents novel developments in the field, as well as practical applications and potential future directions in research and industry. It will be of interest to graduate students and researchers in probability, statistics, and biostatistics, as well as practitioners and technicians in the social sciences, economics, engineering, and medical sciences.
Records
The first and only comprehensive guide to modern record theory andits applications Although it is often thought of as a special topic in orderstatistics, records form a unique area, independent of the study ofsample extremes. Interest in records has increased steadily overthe years since Chandler formulated the theory of records in 1952.Numerous applications of them have been developed in such far-flungfields as meteorology, sports analysis, hydrology, and stock marketanalysis, to name just a few. And the literature on the subjectcurrently comprises papers and journal articles numbering in thehundreds. Which is why it is so nice to have this book devotedexclusively to this lively area of sta...
Inequalities: Theory of Majorization and Its Applications
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 sin...
Relations, Bounds and Approximations for Order Statistics
Bounds on moments of order statistics have been of interest since Sir Francis Galton (1902) flrst addressed the problem of fairly dividing flrst and second prize money in a competition. The present compendium of results represents our effort to sort the plethora of results into some semblance of order. We have tried to assign priority for results appropriately. We will cheerfully accept corrections. Omissions of interesting results have inevitably occurred. On this too we await (cheerful) corrections. We are grateful to Peggy Franklin (University of California), Janet Leach, Domenica Calabria and Patsy Chan (McMaster University) who shared the responsibility of typing the manuscript. The fln...
Conditional Specification of Statistical Models
Efforts to visualize multivariate densities necessarily involve the use of cross-sections, or, equivalently, conditional densities. This book focuses on distributions that are completely specified in terms of conditional densities. They are appropriately used in any modeling situation where conditional information is completely or partially available. All statistical researchers seeking more flexible models than those provided by classical models will find conditionally specified distributions of interest.
Inequalities
Although they play a fundamental role in nearly all branches of mathematics, inequalities are usually obtained by ad hoc methods rather than as consequences of some underlying "theory of inequalities." For certain kinds of inequalities, the notion of majorization leads to such a theory that is sometimes extremely useful and powerful for deriving inequalities. Moreover, the derivation of an inequality by methods of majorization is often very helpful both for providing a deeper understanding and for suggesting natural generalizations.Anyone wishing to employ majorization as a tool in applications can make use of the theorems; for the most part, their statements are easily understood.
