Ebook: A Concept of Generalized Order Statistics

Order statistics and record values appear in many statistical applications and are widely used in statistical modeling and inference. In addition to these wellknown models, several other models of ordered random variables, known and new ones, are introduced which can be effectively applied, e.g., in reliability theory. The main purpose of this book is to present a concept of generalized order statistics as a unified approach to a variety of models of ordered random variables. Numerous related results on distributional and moment properties of order statistics and record values are found in the literature which are deduced separately. The concept of generalized order statistics, however, enablesa common approach to structural similarities and analogies. Well known results can be subsumed, generalized, and integrated within a general framework. Therefore, the concept of generalized order statistics provides a large class of models with many interesting, important and useful properties for both the description and the analysis of practical problems. Contents: Models of ordered random variables (with applications in reliability theory): order statistics, order statistics with nonintegral sample size, sequential order statistics, record values, krecords, Pfeifer's record model, knrecords from nonidentical distributions, ordering via truncation of distributions, censoring schemes / generalized order statistics / distribution theory of generalized order statistics / moments of generalized order statistics / existence of moments / characterization of distributions by sequences of moments / recurrence relations for moments and characterizations of distributions / inequalities for moments and characterizations of distributions / reliability properties: transmission of aging properties, partial ordering of generalized order statistics

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Order statistics and record values appear in many statistical applications and are widely used in statistical modeling and inference. In addition to these wellknown models, several other models of ordered random variables, known and new ones, are introduced which can be effectively applied, e.g., in reliability theory. The main purpose of this book is to present a concept of generalized order statistics as a unified approach to a variety of models of ordered random variables. Numerous related results on distributional and moment properties of order statistics and record values are found in the literature which are deduced separately. The concept of generalized order statistics, however, enablesa common approach to structural similarities and analogies. Well known results can be subsumed, generalized, and integrated within a general framework. Therefore, the concept of generalized order statistics provides a large class of models with many interesting, important and useful properties for both the description and the analysis of practical problems. Contents: Models of ordered random variables (with applications in reliability theory): order statistics, order statistics with nonintegral sample size, sequential order statistics, record values, krecords, Pfeifer's record model, knrecords from nonidentical distributions, ordering via truncation of distributions, censoring schemes / generalized order statistics / distribution theory of generalized order statistics / moments of generalized order statistics / existence of moments / characterization of distributions by sequences of moments / recurrence relations for moments and characterizations of distributions / inequalities for moments and characterizations of distributions / reliability properties: transmission of aging properties, partial ordering of generalized order statistics

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Order statistics and record values appear in many statistical applications and are widely used in statistical modeling and inference. In addition to these wellknown models, several other models of ordered random variables, known and new ones, are introduced which can be effectively applied, e.g., in reliability theory. The main purpose of this book is to present a concept of generalized order statistics as a unified approach to a variety of models of ordered random variables. Numerous related results on distributional and moment properties of order statistics and record values are found in the literature which are deduced separately. The concept of generalized order statistics, however, enablesa common approach to structural similarities and analogies. Well known results can be subsumed, generalized, and integrated within a general framework. Therefore, the concept of generalized order statistics provides a large class of models with many interesting, important and useful properties for both the description and the analysis of practical problems. Contents: Models of ordered random variables (with applications in reliability theory): order statistics, order statistics with nonintegral sample size, sequential order statistics, record values, krecords, Pfeifer's record model, knrecords from nonidentical distributions, ordering via truncation of distributions, censoring schemes / generalized order statistics / distribution theory of generalized order statistics / moments of generalized order statistics / existence of moments / characterization of distributions by sequences of moments / recurrence relations for moments and characterizations of distributions / inequalities for moments and characterizations of distributions / reliability properties: transmission of aging properties, partial ordering of generalized order statistics
Content:
Front Matter....Pages 1-9
Introduction....Pages 11-19
Generalized Order Statistics....Pages 20-86
Moments of Generalized Order Statistics....Pages 87-114
Recurrence Relations for Moments of Generalized Order Statistics and Characterizations of Distributions....Pages 115-144
Inequalities for Moments of Generalized Order Statistics and Characterizations of Distributions....Pages 145-166
Reliability Properties of Generalized Order Statistics....Pages 167-183
Back Matter....Pages 184-212

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Order statistics and record values appear in many statistical applications and are widely used in statistical modeling and inference. In addition to these wellknown models, several other models of ordered random variables, known and new ones, are introduced which can be effectively applied, e.g., in reliability theory. The main purpose of this book is to present a concept of generalized order statistics as a unified approach to a variety of models of ordered random variables. Numerous related results on distributional and moment properties of order statistics and record values are found in the literature which are deduced separately. The concept of generalized order statistics, however, enablesa common approach to structural similarities and analogies. Well known results can be subsumed, generalized, and integrated within a general framework. Therefore, the concept of generalized order statistics provides a large class of models with many interesting, important and useful properties for both the description and the analysis of practical problems. Contents: Models of ordered random variables (with applications in reliability theory): order statistics, order statistics with nonintegral sample size, sequential order statistics, record values, krecords, Pfeifer's record model, knrecords from nonidentical distributions, ordering via truncation of distributions, censoring schemes / generalized order statistics / distribution theory of generalized order statistics / moments of generalized order statistics / existence of moments / characterization of distributions by sequences of moments / recurrence relations for moments and characterizations of distributions / inequalities for moments and characterizations of distributions / reliability properties: transmission of aging properties, partial ordering of generalized order statistics
Content:
Front Matter....Pages 1-9
Introduction....Pages 11-19
Generalized Order Statistics....Pages 20-86
Moments of Generalized Order Statistics....Pages 87-114
Recurrence Relations for Moments of Generalized Order Statistics and Characterizations of Distributions....Pages 115-144
Inequalities for Moments of Generalized Order Statistics and Characterizations of Distributions....Pages 145-166
Reliability Properties of Generalized Order Statistics....Pages 167-183
Back Matter....Pages 184-212
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