Construction Of The Support Set And Correlation Analysis About The Shuffles Of M

Copula function joins bivariate joint distribution function to their one-dimensional marginal distribution function. Bivariate joint distribution function can be given according to copula function and marginal distribution function. Using cop-ula function, the correlation between random variables is discussed. Copula function can be used to generate (u, v) ordered pairs in order to simulate the joint distribution function. Thus more and more attention is given to copula function.As a special class of singular copula function, the shuffles of M is studied in this article. Firstly, utilizing the geometric methods of constructing copula function, the definition and properties of the shuffles of M is given. The function expression between the random variables of the shuffles of M is given by the support set of the shuffles of M. A formula of correlation coefficient is derived. Specially, the power series representation about random variables is given in two equal circumstances; any a copula function can be approximated arbitrarily closely and uniformly by certain shuffles of M. The selection method of the shuffles of M is given in this article. Sec-ondly, using Sklar theorem, we give out the function expression and the formula of correlation coefficient about random variables whose copula function is a shuffle of M. As last, the conclusion is applied to special example.