springer series in statistics an introduction to copulas

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1、ContentsPrefacetotheFirstEditionviiPrefacetotheSecondEditionix1Introduction12DefinitionsandBasicProperties72.1Preliminaries72.2Copulas10Exercises2.1-2.11142.3Sklar’sTheorem172.4CopulasandRandomVariables24Exercises2.12-2.17282.5TheFréchet-HoeffdingBoundsforJ

2、ointDistributionFunctionsofRandomVariables302.6SurvivalCopulas32Exercises2.18-2.26342.7Symmetry362.8Order38Exercises2.27-2.33392.9RandomVariateGeneration402.10MultivariateCopulas42Exercises2.34-2.37483MethodsofConstructingCopulas513.1TheInversionMethod513.1

3、.1TheMarshall-OlkinBivariateExponentialDistribution523.1.2TheCircularUniformDistribution55Exercises3.1-3.6573.2GeometricMethods593.2.1SingularCopulaswithPrescribedSupport593.2.2OrdinalSums63Exercises3.7-3.13643.2.3ShufflesofM673.2.4ConvexSums72Exercises3.14

4、-3.20743.2.5CopulaswithPrescribedHorizontalorVerticalSections763.2.6CopulaswithPrescribedDiagonalSections84xiiContentsExercises3.21-3.34863.3AlgebraicMethods893.3.1PlackettDistributions893.3.2Ali-Mikhail-HaqDistributions923.3.3ACopulaTransformationMethod943

5、.3.4ExtremeValueCopulas97Exercises3.35-3.42993.4CopulaswithSpecifiedProperties1013.4.1HarmonicCopulas1013.4.2HomogeneousCopulas1013.4.3ConcaveandConvexCopulas1023.5ConstructingMultivariateCopulas1054ArchimedeanCopulas1094.1Definitions1094.2One-parameterFami

6、lies1144.3FundamentalProperties115Exercises4.1-4.171324.4OrderandLimitingCases1354.5Two-parameterFamilies1414.5.1FamiliesofGenerators1414.5.2RationalArchimedeanCopulas146Exercises4.18-4.231504.6MultivariateArchimedeanCopulas151Exercises4.24-4.251555Dependen

7、ce1575.1Concordance1575.1.1Kendall’stau158Exercises5.1-5.51655.1.2Spearman’srho167Exercises5.6-5.151715.1.3TheRelationshipbetweenKendall’stauandSpearman’srho1745.1.4OtherConcordanceMeasures180Exercises5.16-5.211855.2DependenceProperties1865.2.1QuadrantDepen

8、dence187Exercises5.22-5.291895.2.2TailMonotonicity1915.2.3StochasticMonotonicity,CornerSetMonotonicity,andLikelihoodRatioDependence195Exercises5.30-5.392045.3OtherMeasuresofAssociation2075.3.1Measureso