极端顺序统计量的渐近理论（英文版）

　　本书是中国科学院推荐的研究生原版教材之一．书中对极端顺序统计量的渐近理论作了详细介绍，尤其注重数学方法和结论在各实际领域中的应用，第二版还特别补充了该领域的一些最新发展．本书只要求读者具有微积分和概率论的知识，因此适合理工类各专业的研究生使用。

暂缺《极端顺序统计量的渐近理论（英文版）》作者简介

Notationsandconventions
INTRODUCTION:ESTIMATESINTHEUNIVARIATECASE
1.1Problemsleadingtoextremevaluesofrandom
variables
1.2Themathematicalmodel
1.3Preliminariesfortheindependentandidentically
distributedcase
1.4Boundsonthedistributionofextremes
1.5Illustrations
1.6Specialpropertiesoftheexponentialdistributionin
thelightofextremes
1.7Surveyoftheliterature
1.8Exercises
2.WEAKCONVERGENCEFORINDEPENDENTANDIDENTICALLY
DISTRIBUTEDVARIABLES
2.1Limitdistributionsformaximaandminima:
sufficientconditions
2.2Otherpossibilitiesforthenormalizingconstantsin
Theorems2.1.1-2.1.6
2.3Theasymptoticdistributionofthemaximumand
minimumforsomespecialdistributions
2.4Necessaryconditionsforweakconvergence
2.5Theproofofpart(iii)ofTheorem2.4.3
2.6Illustrations
2.7Furtherresultsondomainsofattraction
2.8Weakconvergenceforthekthextremes
2.9Therangeandmidrange
2.10Speedofconvergence
2.11Surveyoftheliterature
2.12Exercises
3.WEAKCONVERGENCEOFEXTREMESINTHEGENERALCASE
3.1Anewlookatfailuremodels
3.2Thespecialroleofexchangeablevariables
3.3Preparationsforlimittheorems
3.4Alimittheoremformixtures
3.5Atheoreticalmodel
3.6Segmentsofinfinitesequencesofexchangeable
variables
3.7Stationarysequences
3.8StationaryGaussiansequences
3.9LimitingformsoftheinequalitiesofSection1.4
3.10Minimumandmaximumofindependentvariables
3.11Theasymptoticdistributionofthekthextremes
3.12Someappliedmodels
3.12.1.Exactmodelsviacharacterization
theorems
3.12.2.Exactdistributionsviaasymptotictheory
(strengthofmaterials)
3.12.3.Strengthofbundlesofthreads
3.12.4.Approximationbyi.i.d.variables
3.12.5.Timetofirstfailureofapieceofequipment
withalargenumberofcomponents
3.13Surveyoftheliterature
3.14Exercises
4.DEGENERATELIMITLAWS;ALMOSTSURERESULTS
4.1Degeneratelimitlaws
4.2Borel-Cantellilemmas
4.3Almostsureasymptoticpropertiesofextremesof
i.i.d.variables
4.4Lirasupandliminfofnormalizedextremes
4.5Theroleofextremesinthetheoryofsumsof
randomvariables
4.6Surveyoftheliterature
4.7Exercises
5.MULTIVARIATEEXTREMEVALUEDISTRIBUTIONS
5.1Basicpropertiesofmultivariatedistributions
5.2Weakconvergenceofextremesfori.i.d.random
vectors:basicresults
5.3Furthercriteriaforthei.i.d.case
5.4OnthepropertiesofH(x)
5.5Concomitantsoforderstatistics
5.6Surveyoftheliterature
5.7Exercises
6.MISCELLANEOUSRESULTS
6.1Themaximumqueuelengthinastablequeue
6.2Extremeswithrandomsamplesize
6.3Recordtimes
6.4Records
6.5Extremalprocesses
6.6Surveyoftheliterature
6.7Exercises
APPENDIXES
I.SOMEBASICFORMULASFORPROBABILITIESAND
EXPECTATIONS
II.THEOREMSFROMFUNCTIONALANALYSIS
III.SLOWLYVARYINGFUNCTIONS
REFERENCES
INDEX