Parameter Estimation And Application Of Binary Model Based On Clayton Copula

Survival analysis is widely used in medicine,economic finance,engineering,sociology and other aspects.The Hazard function of many survival variables in survival analysis is bathtub type,such as mortality,machine life,etc.As a generalization of Weibull Distribution and Type I Extreme Value Distribution,Modified Weibull Distribution can better fit the data of bathtub-shaped hazard fuction than other distributions.The survival data has always involved dependency,that is,survival variables are interrelated.Copula function is used to describe the correlation between these variables,which can cover all the dependence information.Therefore,this dissertation selects the Copula function to establish the two-dimensional joint survival model,so as to portray the dependence between survival variables,which is of interest and has practical significance.In this dissertation,we consider the Modifified-Weibull Distribution as the marginal distribution,and the Clayton-Modified-Weibull(CMW)model is established based on Copula function.The parameter estimation and practical application of the CMW model are constructed and studied.Firstly,the structure and properties of the CMW model are introduced,including distribution function,survival function,harzard function,distribution moment and dependence property.Secondly,the data usually has a censored structure in survival analysis,so the parameter estimation including maximum likelihood estimation(MLE)and Inference Functions for Margins(IFM)of CMW model are discussed and numerically simulated under random rightcensored samples.Finally,by verifying the effects of the two estimation methods,and comparing the advantages and disadvantages in the estimation of correlation parameter,the simulation results show that with the increasing of the sample size,the BIAS and MSE decrease,and it’s seen that IFM performed better for estimating correlation parameter.According to the Kaplan-Meier estimation curve,it can be preliminarily judged that the data provided by the US team of diabetic retinopathy are suitable for fitting using the CMW model.By comparing Bayesian Information Criterion(BIC)of the CMW,Marshall-Olkin two-dimensional exponential distribution,Marshall-Olkin two-dimensional Weibull distribution,Freud two-dimensional exponential distribution,Freud two-dimensional Weibull distribution model on the same data,it is concluded that compared with other models,the CMW model is better in fitting the example data,which verifies the practicability of the CMW model.