Research On Composite Construction Of Archimedean COPULA' Generators

Dependence relations between random variables is one of the most widely studied subjects in probability and statistics. The non- parameter properties between variables can be expressed by Copula, so the research of dependence just is the study of properties of Copula. But the traditional correlation coefficients have some limits for a measure of the dependence between random variables. Using Copula for measuring dependence takes more attentions in recent years. There is a great important class of Copulas, called as Archimedean Copula which has many powerful unique properties, for example, symmetry and associative. According to such characteristics, Archimedean Copulas can be constructed, by needed only find the corresponding functions that will serve as generators.Because this, it is meaningful of constructing multivariate Copulas. The theorems of Archimedean Copulas' construction have not been solved completely, even for the special sub-class. Although there exist many ways about constructing bivariate Archimedean Copulas, such as Markov and Laplace transform, et al, have limits to some degree.This paper belongs to the theory research on the construction of Archimedean Copulas' generators. A new method to construction based on function composite is given, that is, generator composited with general elementary functions. As long as found these functions to satisfy the composite construction condition, the new generators might be constructed, so do the corresponding Archimedes Copulas.Firstly, this article introduced the preparation knowledge of dual, multi-dimensional Copula and the Archimedes Copula and the current research situation. Secondly, the method of constructing 2-Copulas was given and the sufficient and necessary conditions were presented. Then the construction procedures were extended to multivariate, and also for the sufficient conditions. And we have discussed some immanent relations of composite constructions and with the other methods. Meanwhile, the dependent properties of the bivariate Copulas constructed by this way also were explored. Moreover, analogied raised and the structure thought proposed the "average generator" structure method, as well as in view of inderivative situation the "comparison generator" method.