FGM Copula的生成与拓展

Generation and Prolongation of FGM Copula

从Copula的构造方法出发,本文引出四类性质不同,形态各异的Copulas。证明了FGM Cop-ula可以由它们生成,从而兼有这四类Copulas的性质。进一步,以FGM Copula及其联合生存函数为基础,应用Copula的几何构造方法拓展出一系列二参数三次幂的广义FGM Copulas。最后,从理论上说明FGMCopula是一个性质非常优良的Copula,在建模时被广泛应用。

In this paper we present four families of copulas by utilizing methods for constructing copulas, it is shown that FCM （Farlie-Gumble-Morgensterm） copula can be derived from these copulas and has their special properties. Using geometric methods, we obtain a series of bivariate copulas with cubic sections and two-parameters on the basis of the FGM copula and its joint survival function. Last, we illustrate that FGM copula has some excellent analytical properties, which can be widely used in modeling.