The Relationship Between Copula Functions And "n-increasing" Functions And Its Related Properties

After half a century of development,Copula functions have become a powerful tool and play a vital role in many fields today.In particular,Copula functions have been more widely used than the traditional correlation coefficients,because they do not require the edge distribution of random variables to follow the same distribution,etc.And many people engage in its research work now.So far,There are no “ideal Copula functions”.We need to select the more effective functions in practical application,resulting in a lot of Copula functions of different forms.In this paper,we give a systematic introduction to the relevant theory and important properties of copula functions,and focus on examples to illustrate its feasible construction method.The multivariate functions with the “n-increasing” property are special.It is different from the requirement that the multivariate functions monotonously increase for each independent variable,but a restriction on independent variable about how they affect the function.The construction of the “n-increasing”functions are of great significance to help us study multivariate functions.In this paper,we construct an “n-increasing” multivariate function,then analyze its relationship with the Copula functions.Following this idea,we give a Copula function with many examples.