Order Statistics, Third Edition

475 Pages·2003·4.59 MB·English

by  H. A. David, H. N. Nagaraja(auth.), Walter A. Shewhart, Samuel S. Wilks(eds.)

Onder Statistics
This Bin
WILEY SERIES IV MROBAMILITY AND STATISTICS
Esublabed by WALTER A. SUEWHTAHTand SAMUBL S. WILkS
said 1 Balding Not 4. ©. Cra, Nichols Fisker,
In lactone. Rasen Lote M Ayan, Dvd Son
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Order Statistics
Third Edition

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Contents

PREFACE

INTRODUCTION
LT The subject of onder sausitex
12. The scope and limits of this book
13 Notation

4 Byerises

BASIC DISTRIBUTION THEORY

2 Distribution of single andor statistic

2.2 Joint distribution af hwo oF more onder staistcs

23 Distribution of the range ened of ether systematic.

24 Onder statistics for a diserete parent

2S Conditional distributions, onder statistics as Markov
chain, and independence results

26 Related satstics

27 Exercises

EXPECTED VALUES AND MOMENTS
BL Baste foruuloe
42 Spaciat consinuots distributions
33° The discrete case
324 Recurrence relations
5 Rrercises
BOUNDS AND APPRUXIMATIONS FOR MOMENTS
‘OF ORDER STATISTICS
4.1 Introduction
42 Distribasion-free bounds for the moments of order

43

44
45

46

a7

statistics ond of the range
Bounds and appresimations by orthogonal inverse
expunsion

Stochastic orderings

Bounds forthe expected values of enter statistics in
erm of quantiles ofthe parent distraction
Apprasimations to momen in terms ofthe quantile
Fenelon and is derivaives

Exercises

‘THE NONIID CASE

31
$2

36

Introduction

Onder statistics for independent nonidentically
discribueed variates

Order staisties for dependent variates

Inequalities and recurrence relations—nam-HD cases
Ronnds for linear functians of under statistics and for
their expected values

Rxercises

FURTHER DISTRIBUTION THEORY

fa
62
63
64
65
66

Iravoduetion
Stadentication

Statitics expressible ax mums
Random division of un interval
Linear functions of ander statinion
Moving onder statisties
conrens

67 Charaterizations 1?
68 Concomizants of onder staistics yaa
69 Exercises 18

‘ORDER STATISTICS IN NONPARAMETRIC

INFERENCE 159
71 Distritusion free confidence intervals for quantiles 159
7.2 Distribution free totorance intorvats 164
7.3 Distribution free prediction intervals 167
74° Exercises 169

ORDER STATISTICS IN PARAMETRIC INFERENCE 171

81 Introduction and basic results 178
82 Information in onder statistics 180
83 Bootverap estimation of quanctes and of moments of

tarde statistics 183
84 Least-squares extimation of lovation and scale

parameters by onder statistics 185
5 Estimation of location and scale parameters for

censored data it
86 Life tening, with special emphasis on the expmentiat

distribution 204
87 Prediction of onder statistics 208
88 Robust extimation a
89° Brercises 223
SHORTCUT PROCEDURES 238
DL Imroducrion 239
22 Quick measures of tcation 2a
9.3 Range and mean range as measures oftispersion 242
94 Other quick measures of dispersion 248
25 Quick esimanes in bivariate samples 250
9.6 The sudensced range 258
97 Quick teas 2357

98 Ranbed-vet sampling 262
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it

covrenns

wo
919
gat
92

O-staistcs and L-moments in date summertzatton
Probability plowing and tess of goodness of ft
Statistical quatiy coneot

Exercises

ASYMPTOTIC THEORY

Ir
402
103
joa
105
108
107
108
109

Introduction
Representations for the ceniral sample quantes
Asymptotic joint distribution of central quantiles
Optimal choice of order seatiticn ix large samples
The asympotc distribution ofthe extreme

‘The asympiotc joist disiribtation of extremes
Extreme-value thuory for dependent sequences
Asymprotic propertics of intermediate order siaristes
Asymptotic results for multivariate samples

10.10 Baercives

ASYMPTOTIC RESULTS FOR FUNCTIONS
OF ORDER STATISTICS

us
uz

3
ud

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m7
us

Introduction
Asympiotie distribution ofthe range, midrange, and
spacings

Limit distribution of the eimned mean

Asymptutic normality of linear functions of onder
Gptimat asymptonc estimation by order statisties
Estimarors of tai index and extreme quansites
Asymptotic theory of concomiants of order statistics
Exercives

APPENDIX: GLTDY. TO TABLES AND ALGORITHMS

REFERENC)

Bu
33
3S

323

323

ide
29

337
335
sar
35
350
385
367

451
Preface to Third Edition

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