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262()Vol.26,No.220076JournalofXinjiangNormalUniversityJun.2007(NaturalSciencesEdition)Copula1,2(1.,831100;2.,510006)3:CopulaCopula,CopulaCopula:;;Copula;;:O211:A:1008296592(2007)20220015204,XY:=Cov(x,y)Var(x)Var(y)=E(x-Ex)(y-Ey)Var(x)Var(y)(1)(x1,y1),,(xn,yn),XY(1),,XY,,,,(Cauchy),,,,,CopulaCopula,,,,,,Copula,()Copula,CopulaCopula,Copula1Copula1.1Copula,Copula,(,3[]2006-11-24[](No.10671044),(No.2004J1-C0333),(No.2004)[](1949-),,,,()2007[1]):CopulaC:[0,1]2[0,1](1)u,v[0,1],,C(u,0)=C(0,v)=0,C(u,1)=C(1,v)=1;(2)u1,u2,v1,v2[0,1],u1Fu2,v1Fv2,C(u2,v2)-C(u2,v1)-C(u1,v2)+C(u1,v1)E0SklarCopulaSklar:F,F1F2,CopulaCx,yR=(-,+),F(x,y)=C(F1(x,)F2(y))(2)F1F2,C,CCopula,F1F2,F,F1F2Sklar,Copula:Copula,[0,1];Copula,,,,,Sklar,()Copula,CopulaXY,CopulaC(u,v)=uv,CopulaCopula,,CopulaCopula,Kendall=k0Fu,vF1C(u,v)dC(u,v)-1,Spearman=121010uvdC(u,v)-3,Ginir=4(10C(u,1-u)du-10(u-C(u,u))du),=4C(12,12)-11.2CopulaCopula(Copulat-Copula)ArchimedeanCopulaArchimedeanCopula,Copula::[0,1][0,):,u[0,1](u)0,[-1](t)=-1(t)0FtF(0)0(0)FtFC(u,v)=[-1]((u)+(v))CopulaCopula,Copula(t)=(-lnt),[1,]CopulaCumbelCopula,CG(u,v;a)=exp{-[(-logu)1/a+(-logv)1/a]a},a(0,1],a=1,uv;a0,uv(t)=(t--1)/,E1,CopulaClaytoncopula,C(u,v)=(u-+v--1)-1,E-102Copula,(X,Y)F(x,y),f(x,y),F1(x)F2(y),f1(x)f2(y),CopulaC(u,v)c(u,v),f(x,y)=c(F1(x),F2(y))f1(x)f2(y),(3)c(u,v)=52C(u,v)5u5v(3),f(x,y),CopulaC(u,v)c(u,v),XY;612Copulaf1(x)f2(y){(Xi,Yi),i=1,2,,n}(X,Y),l=ni=1lnc(F1(Xi),F2(Yi))+ni=1[lnf1(Xi)+lnf2(Yi)](4)(X,Y),(4),,Copula2.1EMLCopulaC(u,v;)=(-1(u),-1(v)),u,v(0,1),Copulac(u,v;)=121-2exp{--2[(-1(u))2+(-1(v))2-2-1(u)-1(v)2(1-2)},,-1F1(x)F2(y),Sklar,F(x,y;)=C(F1(x),F2((y);)=(-1(F1(x)),-1(F2(y))),(5),F1(x)F2(y)l()=nl=1{-ln2-12ln(1-2)-2(z21i+z22i)-2z1iz2i2(1-2)}+ni=1[lnf1(Xi)+lnf2(Yi)](6)z1i=-1(F1(Xi)),z2i=-1(F2(Yi)),EML(ExactMaximunLikelihood)Copuladl()d=0(7)l()^EML,,,,,2.2IFMF1(x;)F2(y;),f1(x;)f2(y;),Copula,l(,,)=l1(,)+l2(,,),(8)l1(,)=ni=1lnf1(Xi;)+ni=1lnf2(Yi;),(9)l2(,,)=-nln(2)-n2ln(1-2)-ni=12(z21i+z22i)-2z1iz2i2(1-2),(10)z1i=-1(F1(Xi;)),z2i=-1(F2(Yi;))l1(,);l2(,.),,,=(,,)EML^=(^,^,^):^=argmaxl()(11),,,Copula,IFM(InferenceFunctionforMargins)[2]IFM,IFM,=(,,)^=(^,^,^),:55l1(,)=0,55l1(,)=0,l1(,),71()2007:,,55l2(,^,^)=0,l2(,^,^)Copula^2.3MBPIFMEML,,,IFM,MBP(MaximizationbyParts)[3]MBPIFM,,,MBP,MBP,=(,,)^=(^,^,^),:551l1(1)=0,l1(,)^(1)1=((1),(1)):^(1)1=((1),(1)),55l2(,^(1),^(1))=0,l2(,^(1),^(1))Copula^(1)k-1:(k-1),(k-1),(k-1),551l1(1)+551l2((k-1),^(k-1)1)=0,^(k)1k:55l2(,^(k),^(k))=0,^(k),k=2,,3,=(,,)EMLIFM,MBP3.4,,,Copula^F1(x)^F2(y)F1(x)F2(y),Copula^:dd{-n2ln(1-2)-ni=1[-2(z21i+z22i)-2z1iz2i2(1-2)]}=0,(12)z1i=-1(^F1(Xi)),z2i=-1(^F2(Yi)),^F1(x)=1nni=1I[XiFx],^F2(y)=1nni=1I[YiFy],I[]4Copula,Copula,Copula:[1]Nelsen,R.B..Anintroductiontocopula[M].Springer-Verlag,NewYork,1999.[2]Xu,J.J..Statisticalmodelingandinferenceformultivariatrandlongitudinaldiscreteresponsedata.PhDthesis,StatisticaDepartment,U2niversityofBritishColumbia,1996.[3]Song,P.Y.,Fan,Y.andKalbfleisch,J..Maximizationbypartsinlikelihoodinference[J].JournaloftheAmericanStatisticalAssociation,2005,(100):1145-1167.(24)81()2007RobustExponentialStabilityofReaction-diffusionGeneralizedCohen-GrossbergNeuralNetworkswithDistributedDelaysMAChangxiu(SchoolofMaths-physicsandInformationscienceXinjiangNormalUniversity,UrumqiXinjiang830054)Abstract:Thispaperisabouttherobuststabilitypropertyofreaction-diffusiongeneralizedCohen-Grossbergneuralnetworkswithdistributeddelays.Byemployingthepropertiesoffixpointandinequalitytechnique,somenewcriteriaareobtainedtoensurethegloballyrobustexponentialstability(GRES)ofanequilibriumpoint.Keywords:Exponentialstability;reaction-diffusion;Cohen-Grossbergneuralnetworks;Equilibri2umpoint;distributeddelays.Keywords:Exponentialstability;Reaction-diffusion;Cohen-Grossbergneuralnetworks;Equilib2riumpoint;Distributeddelays.(18)ParametricEstimationofCopulaFunctionYANGYidang1,LUOXianhua2(1.ChangjiCollege,ChangjiXinjiang831100;2.SchoolofMathematicsandInformationScience,GuangzhouUniversity,GuangzhouGuangdong510006)Abstract:Copulatheoryhasbeenbroadlyusedinthestatisticalandfinancialarea.Akeystepinmod2elingmultivariatedistributionfunctionishowtoestimatetheparameterofCopulafunction.InthispaperwediscusstheparametricestimationofCopulafunctionwithsomeexamples.42