阿基米德COPULA生成元的復(fù)合構(gòu)造研究.pdf

1、西南交通大學(xué)碩士學(xué)位論文阿基米德COPULA生成元的復(fù)合構(gòu)造研究姓名：陳崇雙申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：概率統(tǒng)計(jì)指導(dǎo)教師：何平20081201西南交通大學(xué)碩士研究生學(xué)位論文第1I頁AbstractDependencerelationsbetweenrandomvariablesiSoneofthemostwidelystudiedsubjectsinprobabilityandstatisticsThenonparameterpropert

2、iesbetweenvariablescanbeexpressedbyCopula，SOtheresearchofdependencejustisthestudyofpropertiesofCopulaButthetraditionalcorrelationcoefficientshavesomelimitsforameasureofthedependencebetweenrandomvariablesUsingCopulaformea

3、suringdependencetakesmoreattentionsinrecentyearsThereisagreatimportantclassofCopulas，calledasArchimedeanCopulawhichhasmanypowerfuluniqueproperties，forexample，symmetryandassociativeAccordingtosuchcharacteristics，Archimede

4、anCopulascanbeconstructed，byneededonlyfindthecorrespondingfunctionsthatwillserveasgeneratorsBecausethis，itismeaningfulofconstructingmultivariateCopulasThetheoremsofArchimedeanCopulas’constructionhavenotbeensolvedcomplete

5、lyevenforthespecialsub—classAlthoughthereexistmanywaysaboutconstructingbivariateArchimedeanCopulas，suchasMarkovandLaplacetransform，etal，havelimitstosomedegreeThispaperbelongstothetheoryresearchontheconstructionofArchimed

6、eanCopulas’generatorsAnewmethodtoconstructionbasedonfunctioncompositeisgiven，thatis，generatorcompositedwithgeneralelementaryfunctionsAslongasfoundthesefunctionstosatisfythecompositeconstructioncondition，thenewgeneratorsm

7、ightbeconstructed，SOdothecorrespondingArchimedesCopulasFirstlythisarticleintroducedthepreparationknowledgeofdual，multidimensionalCopulaandtheArchimedesCopulaandthecurrentresearchsituationSecondlythemethodofconstructing2C

8、opulaswasgivenandthesufficientandnecessaryconditionswerepresentedThentheconstructionprocedureswereextendedtomultivariate，andalsoforthesufficientconditionsAndwehavediscussedsomeimmanentrelationsofcompositeconstructionsand

9、withtheothermethodsMeanwhile，thedependentpropertiesofthebivariateCopulasconstructedbythiswayalsowereexploredMoreoveranalogiedraisedandthestructurethoughtproposedthe“averagegenerator”structuremethod，aswellasinviewofinderi