Perturbation Copula Correlation Measure And Extreme Value Problem Analysis

Copula is used to connect the random vector with the joint distribution and describe statistical model of the structure of dependence between multiple random variables.It is widely used in economy,financial,education and other fields to study the dependence between the random variable.Extreme value theory is a kind of extreme value in the rear of data modeling theory,they are widely used in statistics,health care,insurance,etc.Copula plays an important role in measuring the correlation of extreme events.The main body of this thesis is divided into two parts.The first part includes chapter 2,chapter 3 and chapter 4,which deeply explores the correlation coefficient in Copula.The main tasks are as follows: summarize the original expression derived from Copula to measure correlation dependence.The paper presents a new type of disturbance Copula constructed by mathematical algebra.Copula is divided into singular and continuous.The correlation measurement of the newly obtained singular Copula and continuous Copula functions is mainly studied.The second part includes chapter 5 and Chapter 6,applying the extreme value model and the Copula to measure the correlation between two extreme events.Chapter 2 constructs a new Copula satisfying all the conditions to make Copula more flexible.The mixed Copula with perturbations is studied to make it more flexible in measurement.Copula is divided into singular Copula and continuous Copula.In chapter 3,we target the singular Copula and add disturbance to it to construct a new Copula.Then,Spearson’s ρ,Kendall’s τ,Blomqvist’s β,Gini’s γ proofs and calculations are given.In Chapter 4,by the same construction of continuous Copula,the expressions of four correlation measures generally applicable are obtained.The paper shows the dependence measure when different values of parameters are taken after perturbations are added to several classic Copula families.In chapter 5,generalized extreme value(GEV)distribution is applied to analyse extreme events.The data of man’s 110 m hurdles were collected and the extreme value model of non-stationary time series was established.In chapter 6,the correlation measurement of two extreme events is studied.Copula model was selected to measure the correlation between the two events according to the data of 110 m hurdles and 100 m competition in track and field events,which overcomes the deficiency of traditional correlation coefficient.In conclusion,the thesis mainly analyzes and discusses the correlation measurement of continuous and singular Copula functions obtained after construction.Extreme value model is applied to the analysis of sports events.Use the Copula to measure correlations between man’s 110 m hurdles competition and 100 m competition.