Copulas With Polynomial Sections And Its Application

The study of Copulas and their application has been made a great development in the past decades. As a tool to describe the dependence of random variable, Copulas play a very important role in Mathematical Modeling and Simulation. So it is very meaningful to construct different kinds of Copulas. Regarding function model with n-th-order polynomial sections as starting point,copulas with polynomial sections are constructed, and some application is also presented.The main contents of this paper include:Firstly, definition of Copulas and some fine properties in statistical analysis are introduced, then the model of linear section, square section and cubic section are analyzed, following, we extended the model to n-th-order polynomial section, and presented two necessary and sufficient conditions for Copulas with n-th-order polynomial section.Secondly, Symmetry properties, measures of association of these copulas are studied as well, and the general formulas of Kendall'sτ, Spearman'sρand Gini'sγfor these copulas are derived. The method to generate sample from specific joint distribution through Copulas theory is discussed too.Finally, families of Kotz and Johnson's iterated FGM copula and normal FGM copula are provided to verify these theorems and properties.