The Construction Of Multivariate Copulas Based On G Function

Dependence relations between random variables is one of the most widely studied subjects in probability and statistics. 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. Actually, copula plays an important role in the study of dependence, it also can be used for constructing multivariate distributions. If there exist a family of copulas, we could construct any bivariate or multivariate distribution functions of given margins by Sklar's theorem and these distributions are always very useful for simulation.Because this, it is meaningful of constructing multivariate copulas. But constructing n-copulas is difficult. Although there exist many ways about constructing bivariate copulas, few of them can extend to multivariate. Some methods about constructing n-copulas in many references have limits to some degree and also complicate premise.This paper gives a new method of constructing n-copulas depends on the law of total probability. The method that constructing n-copulas based on g functions which defined in this paper. We can get n-copulas if a family of g functions could be found. Firstly, this paper introduces the definition and basic properties of copula, and some results about construction of n-copulas in recent years. Secondly, the method of constructing 2-copulas was given, and then extends the construction procedures to n-copulas. And we have discussed some properties of the 2-copulas which construct by this method. Meanwhile all properties of 2-copulas in this paper have n-dimensional analogs. Since the method depends on g functions, finding g functions is the key to constructing n-copulas. Finally this paper have given a method of finding g functions depends on one-dimensional distributions. And the relations between gfunctions and the generators of Archimedean copula were found on someconditions.