The Construction Of Bivariate Copulas Based On Real 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 copulas. But constructing copulas is not worked out exactly. Although there are many ways about ways about constructing bivariate copulas,they are not perfectly. Even if the constructing of Archimedean copula with special form has so much bias in applying,because of its symmetric.This paper construct a new bivariate copula with special form from the mind of Archimedean copula. This new bivariate copula is not symmetric,the relationship of the two distribution functions of bivariate distribution function ismade in the part of the whole function,And the difference between dependence and independence is more exactly. The method of constructing this kind of copula is simple, just need continuous and differentiable real functions. At the same time,some examples are placed in the paper to prove itsexistence. At last,some propeties of this new 2-copula is discussed.