極端順序統(tǒng)計量的漸近理論（英文版）

定　價：￥54.00

作　者：	[]JanosGalambos著
出版社：	科學(xué)出版社
叢編項：	中國科學(xué)院研究生教學(xué)叢書
標(biāo)　簽：	逼近

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ISBN：	9787030089175	出版時間：	2001-01-01	包裝：	平裝
開本：	23cm	頁數(shù)：	414頁	字?jǐn)?shù)：

內(nèi)容簡介

　　本書是中國科學(xué)院推薦的研究生原版教材之一．書中對極端順序統(tǒng)計量的漸近理論作了詳細(xì)介紹，尤其注重數(shù)學(xué)方法和結(jié)論在各實際領(lǐng)域中的應(yīng)用，第二版還特別補充了該領(lǐng)域的一些最新發(fā)展．本書只要求讀者具有微積分和概率論的知識，因此適合理工類各專業(yè)的研究生使用。

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圖書目錄

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