The Construction Of Two New Types Of Copula Family And The Application Of Extreme Value Theory

Copula is the function that join the couple multivariate distribution functions to their one-dimensional marginal distribution functions.Copula theory provides many types of Copula models.Different types of Copula have different mathematical characteristics and can be used to describe different data correlation patterns.In this paper,the construction of two new types of Copula and the application of extreme value theory are studied.For the construction of new Copula functions,we construct bivariate copulas with given values in the left upper corner and lower right corner of the opposite diagonal section,and obtain the best-possible lower bounds for the set of the copulas.It showed that the relationship between the statistics located in the vicinity of the diagonal,and the correlation between extreme events.Furthermore,we introduce the new types of bivariate copulas based on the perturbation of the given copula.By put on the perturbation of the copulas,the new methods of constructions(quasi-)copulas is obtained.In particular,based on the given copula M and ?,we look for the perturbations into another copula.The diagonal section and the opposite diagonal section of the special copula also be studied.For the application of extreme value theory,firstly,based on the Qingdao tide height data from January 2013 to April 2018,a generalized extreme value distribution(GEV)model is established to analyze the monthly maximum value series of Qingdao tidal height.The maximum height of the high tide that may occur in the next 10 months is inferred.Finally,we combine the extremum theory with the copula function,introduce the extrem value copula function,and explore the tail-correlation property of binary extrem variables.