An Introduction to Order Statistics

✍ Scribed by Mohammad Ahsanullah, Valery B Nevzorov, Mohammad Shakil (auth.)

• Publisher: Atlantis Press
• Year: 2013
• Tongue: English
• Leaves: 241
• Series: Atlantis Studies in Probability and Statistics 3
• Edition: 1
• Category: Library

✦ Synopsis

This book presents the theory of order statistics in a way, such that beginners can get easily acquainted with the very basis of the theory without having to work through heavily involved techniques. At the same time more experienced readers can check their level of understanding and polish their knowledge with certain details. This is achieved by, on the one hand, stating the basic formulae and providing many useful examples to illustrate the theoretical statements, while on the other hand an upgraded list of references will make it easier to gain insight into more specialized results. Thus this book is suitable for a readership working in statistics, actuarial mathematics, reliability engineering, meteorology, hydrology, business economics, sports analysis and many more.

✦ Table of Contents

Front Matter....Pages i-x
Basic Definitions....Pages 1-13
Distributions of Order Statistics....Pages 15-21
Sample Quantiles and Ranges....Pages 23-35
Representations for Order Statistics....Pages 37-50
Conditional Distributions of Order Statistics....Pages 51-60
Order Statistics for Discrete Distributions....Pages 61-74
Moments of Order Statistics: General Relations....Pages 75-81
Moments of Uniform and Exponential Order Statistics....Pages 83-94
Moment Relations for Order Statistics: Normal Distribution....Pages 95-103
Asymptotic Behavior of the Middle and Intermediate Order Statistics....Pages 105-113
Asymptotic Behavior of the Extreme Order Statistics....Pages 115-130
Some Properties of Estimators Based on Order Statistics....Pages 131-137
Minimum Variance Linear Unbiased Estimators....Pages 139-151
Minimum Variance Linear Unbiased Estimators and Predictors Based on Censored Samples....Pages 153-161
Estimation of Parameters Based on Fixed Number of Sample Quantiles....Pages 163-168
Order Statistics from Extended Samples....Pages 169-173
Order Statistics and Record Values....Pages 175-188
Characterizations of Distributions Based on Properties of Order Statistics....Pages 189-199
Order Statistics and Record Values Based on F α Distributions....Pages 201-216
Generalized Order Statistics....Pages 217-225
Compliments and Problems....Pages 227-230
Back Matter....Pages 231-244

✦ Subjects

Statistical Theory and Methods; Statistics for Business/Economics/Mathematical Finance/Insurance; Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences; Statistics, general; Econometrics; Biostatistics