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An Introduction to Order Statistics / by Mohammad Ahsanullah, Valery B Nevzorov, Mohammad Shakil
Contributor(s): Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Atlantis Studies in Probability and Statistics ; 3 | SpringerLink BücherPublisher: Paris : Atlantis Press, 2013Description: Online-Ressource (X, 244 p, digital)ISBN:- 9789491216831
- 519.5
- QA276-280
Contents:
Summary: Basic definitions -- Distributions of order statistics -- Sample quantiles and ranges -- Representations for order statistics -- Conditional distributions of order statistics.-Order statistics for discrete distributions -- Moments of order statistics: general relations -- Moments of uniform and exponential order statistics -- Moment relations for order statistics: normal distribution -- Asymptotic behavior of the middle and intermediate order statistics -- Asymptotic behavior of the extreme order statistics -- Some properties of estimators based on order statistics -- Minimum variance linear unbiased estimators -- Minimum variance linear unbiased estimators and predictors based on censored samples -- Estimation of parameters based on fixed number of sample quantiles -- Order statistics from extended samples -- Order statistics and record values -- Characterizations of distributions based on properties of order statistics -- Order statistics and record values based on Fα distributions -- Generalized order statistics -- Compliments and problems.Summary: 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.PPN: PPN: 1028318189Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SXMS | ZDB-2-SMA
An Introduction to Order Statistics; Preface; Contents; 1Basic Definitions; 2Distributions of Order Statistics; 3Sample Quantiles and Ranges; 4Representations for Order Statistics; 5Conditional Distributions of Order Statistics; 6Order Statistics for Discrete Distributions; 7Moments of Order Statistics: General Relations; 8Moments of Uniform and Exponential Order Statistics; 8.1 Uniform order statistics; 9Moment Relations for Order Statistics: Normal Distribution; 10Asymptotic Behavior of the Middle and Intermediate Order Statistics; 11Asymptotic Behavior of the Extreme Order Statistics
12Some Properties of Estimators Based on Order Statistics13Minimum Variance Linear Unbiased Estimators; 14Minimum Variance Linear unbiased Estimators and Predictors Based on Censored Samples; 15Estimation of Parameters Based on Fixed Number of Sample Quantiles; 16Order Statistics from Extended Samples; 17Order Statistics and Record Values; 18Characterizations of Distributions Based on Properties of Order Statistics; 19Order Statistics and Record Values Based on Distributions; 20Generalized Order Statistics; 21Compliments and Problems; Bibliography; Index
Basic definitions -- Distributions of order statistics -- Sample quantiles and ranges -- Representations for order statistics -- Conditional distributions of order statistics.-Order statistics for discrete distributions -- Moments of order statistics: general relations -- Moments of uniform and exponential order statistics -- Moment relations for order statistics: normal distribution -- Asymptotic behavior of the middle and intermediate order statistics -- Asymptotic behavior of the extreme order statistics -- Some properties of estimators based on order statistics -- Minimum variance linear unbiased estimators -- Minimum variance linear unbiased estimators and predictors based on censored samples -- Estimation of parameters based on fixed number of sample quantiles -- Order statistics from extended samples -- Order statistics and record values -- Characterizations of distributions based on properties of order statistics -- Order statistics and record values based on Fα distributions -- Generalized order statistics -- Compliments and problems.
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