One Kind Copula Function And Research Of Relevant Problem

Dependence relation between random variables is the main subject in Probability and Statistics. The joint distribution of random variables can totally tell us the distribution of its components and the dependence relation between them. For multivariate random variables, it is difficult to fix on their joint distribution, though we can easily get its marginal distributions. It is essential to study the distributions and the dependence relation between them respectively. Copula theory provides good solutions.This paper obtains a sufficient condition of Copula function based on the theory of copula, presents one kind copula function----the quadrant-copula function. Main tasks are as follows:First, the paper gives a sufficient condition of Copula function.Second, Based on the analysis of the definition of copula function as well as the discussion of the dual of a copula, survival copula, Co-copula, the quadrant-copula function connected with the copula function is presented. The relationship between the quadrant-copula and the general copula is given mainly, and gives a method of obtaining Copula bounds. its bounds, upper and lower bounds also are presented when its value at a single point is known. Some important properties of the quadrant-copula are discussed under strict monotone transformation on its random variables.Third, the paper provides the equation of the quadrant-copula based on the Archimedean Copulas, and dependence measure based on the quadrant-copula. The relationship between the Kendall's correlation coefficient of quadrant-copula and the Kendall's correlation coefficient of the general copula is given, the result of tail-dependence coefficient based on the quadrant-copula, and the relationship between the Spearman's correlation coefficient of quadrant-copula and the Spearman's correlation coefficient of the general copula is given...