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This book emphasizes the use of stochastic orders as motivational tools for developing new statistical procedures. Stochastic orders have found useful applications in many disciplines, including reliability theory, survival analysis, risk theory, finance, nonparametric methods, economics and actuarial science. Written by a statistician, this volume clarifies the connection between stochastic orders and nonparametric methods.
The importance of order statistics and spacings is well recognized. Classically, they mainly focus on the case when the observations are independent and identically distributed, however, several new developments have extended the comparison of order statistics to the case of non-identically distributed or non-independent observations. In addition to giving a detailed discussion of various topics in the general area of stochastic orders, a substantial part of the book is devoted to recent research on stochastic comparisons of order statistics andspacings, including a long chapter on dependence among them.
The book will be useful for graduate students and researchers in statistics, economics, actuarial science and other related disciplines. In particular, with close to 300 references, it will be a valuable resource for reliability theorists, applied probabilists and statisticians. Readers are expected to have taken a first-year graduate level course in mathematical statistics or in applied probability.
Sommario
Introduction and Preliminaries.- Magnitude Orders.- Variability Orders.- Skewness and Relative Aging Orders.- Dependence Orders.- Stochastic comparisons of sample spacings.- Dependence among order statistics and spacings.- Stochastic Comparisons of Weighted Sums of Random Variables.- Stochastic comparisons of mixtures of distributions.
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Subhash C. Kochar currently teaches at Portland State University. He has been a faculty member at the Indian Statistical Institute and the Panjab University, and has been a visiting professor at many well-known universities worldwide. His research interests are in stochastic orders, reliability theory, mathematical statistics and nonparametric inference. The originator of some of the most popular and widely used concepts in the above areas, he has collaborated with many noted experts, and has an extensive list of publications in leading Statistics and Probability journals. He has been on the editorial boards of several Statistics and Probability journals.
