Research On Extreme Copula Theory And Its Applicatio

Copula is the residual information of multivariate joint distribution function after removing the edge distribution,which completely describes the correlation structure between random variables.A series of correlation indexes derived from it can capture nonlinear correlation and tail correlation between random variables.A large number of copulas with different structural characteristics have been constructed for modeling in order to accurately fit the relevant structures of actual problem data.Extremum statistics mainly studies the statistical regularity of extreme events that rarely happen,but can have important effects once they happen,that is,studies the tail change law of random variables.Copula plays an important role in constructing multivariate extremum distribution models.In this paper,the perturbation construction of some singular Copula and the application of extremum theory are studied.Singular Copula refers to a class of Copula whose density function is 0.Due to its complex structure representation,few literatures have been studied,but it plays an important role in the study of boundness of Copula.In this paper,the disturbance structures of several types of singular Copula are studied,including the drag supported on two line segments,the drag based on M,the drag supported on arc and the drag based on M on n line segments.Firstly,four concordency measuresτ,ρ,γ,β and correlation measures σ of these four types of Copula are studied,and the independent relationship between various random variables of Copula is deduced by σ.Then,the value range variation of various Copula measures τ,ρ,γ,β,σ for different parameter values is analyzed.Secondly,a new disturbance Copula is constructed by adding disturbance terms to the four types of Copula.Then,the correlation measureτ,ρ,γ,β,σ and the relationship between them are explored.Compared with the original Copula function,it is concluded that the correlation σ between random variables has a more direct and effective optimal and better value range compared with other several types of measures.Aiming at the application of extremum theory.Firstly,the generalized Pareto model was used to fit the electricity load data of Tianjin in 2019,and the unitary extreme value distribution model was established to obtain the estimated values of the average electricity load at the recurrence level and beyond the recurrence level.It is helpful to optimize the power generation plan and realize the reasonable allocation of resources.Then,the unary extreme value distribution is combined with Copula to analyze the extreme value correlation of the two influencing factors of daily mean temperature and daily rainfall,and the binary superthreshold model of the two factors is established.The joint distribution function is obtained,the tail edge probability and conditional probability are solved,and the influence of these factors on electricity load is understood theoretically.