Study For The Dependence Of Tail Dependence Random Variables According To Copula

Copulas are widely paid attention in recent years as a method which describes dependence of random variables. Its emergence makes the description of dependence between random variables perfect .But copula can be used not only in probability, statistics and stochastic processes but also in many other fieldsIn many pratical problems it concerns about the dependence of tail denpendence random variables. Correlation coefficientρaccording to Pearson, Sperrman's rank correlationρ_sp and Kendall's coefficentτall can quantitive measure dependence of random variables by copula, but in some situation the method can't catch exactly the dependence case of random variables. Lower tail dependence coefficient and upper tail denpendence coefficient are more specialized descriptin. So it's very important to estimate the lower tail coefficient by observation values.Therefore this thesis invetigates the relation of copula and its extreme tail copula, the generator of Achimedean copula and regular variation from the definition of truncation copula and extreme tail copula. Meanwhile the relation of the generator of extreme tail copula and regular variation is obtained according to its correlative properties. Then the thesis emphasizely investigates the properties of lower tail coefficient and its parametric estimation and non-parametric estimation and the consistence of non-parametric estimation. Finally the copula which is corresponding to lower tail random variables is applied in actuarial science and some models of survival function are constructed.