# A Concept of Generalized Order Statistics

• Udo Kamps
Textbook

Part of the Teubner Skripten zur Mathematischen Stochastik book series (TSMS)

1. Front Matter
Pages 1-9
2. Udo Kamps
Pages 11-19
3. Udo Kamps
Pages 20-86
4. Udo Kamps
Pages 87-114
5. Udo Kamps
Pages 167-183
6. Back Matter
Pages 184-212

### Introduction

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

### Keywords

DEX Distribution Moment Statistik Symbol Zuverlässigkeit

#### Authors and affiliations

• Udo Kamps
• 1
1. 1.Rhein.-Westf. Techn. HochschuleAachenGermany

### Bibliographic information

• DOI https://doi.org/10.1007/978-3-663-09196-7
• Publisher Name Vieweg+Teubner Verlag, Wiesbaden
• eBook Packages
• Print ISBN 978-3-519-02736-2
• Online ISBN 978-3-663-09196-7
• Series Print ISSN 1615-4193
• Buy this book on publisher's site
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