极端顺序统计量的渐近理论（英文版）

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