On The Construction Of Bivariate Copula Function With Application

Copula is a multivariate function connecting multidimensional joint distribu-tion and one-dimensional marginal distribution between variables,this paper mainly studies the construction and application of bivariate Copula function.Considering the limitation of the construction of Copula function at present,this paper puts forward the methods of constructing bivariate Copula function from the angle of function and transformation respectively,and ap-plies the combination of Copula function and score test method to diagnose the mean shift of random variables.Based on the Copula function model theory,this paper does the following research:(1)From the perspective of function,the construction method of bivariate Copula function based on class G function is proposed.Firstly,we present the definition of class G function,discuss its some properties,and design several specific class G functions accordingly,then construct a new bivariate Copula function based on class G function,at the same time,the data of the output value of the primary industry in Chengdu and Mianyang City are selected,and the correlation of regional output value is empirically analyzed by using different bivariate Copula functions.The results show that the Copula function constructed by class G function has good representativeness in the correlation problem of measuring variables.(2)From the point of view of transformation,the construction of the generator of Archimedes Copula is improved and studied.Five kinds of generators of Archimedes Cop-ula function are constructed based on unilateral Laplace transform,bilateral Laplace transform and Z-transformation,and Archimedes Copulas based on five kinds of generators are derived.This method expands the way to construct the generator of Archimedes Copula function and extends the research scope of Archimedes Copula function.(3)Using the principle of control chart,an on-line monitoring method of score test based on bivariate Copula function is proposed.Firstly,the joint density function between two random variables is constructed by using a bivariate Copula function,then the likelihood function is established,and on the basis of the likelihood function structure score test test statistics,detection of the two random variables mean whether drift in the statistical process.In the simulation experiment,Hotelling T2 control chart was used for comparison,considering the size of the second type of error under the control of the first type of error,that is,the change of the average running length under the state of process out of control.The results show that score test is more sensitive in detecting small drift,and can send out abnormal warning signal as early as possible when the process is out of control,which has better diagnosis effect.