Parameter Estimation Of Dependent Type ? Interval Censored Data Based On Copula Function

Due to the limitation of objective reasons,the data related to the failure time often can not get the accurate value,and the sample is often a group of interval censored data.The types of censoring are divided into independent censoring and dependent censoring.As the name suggests,independent censoring means there is no correlation between them.There are a lot of research results about interval censored data,but most of them are obtained under the assumption of independent censoring.If we use the statistical method of independent censoring for dependent interval censored data,we will ignore a lot of information about dependence.In this paper,we will use copula model to analyze the dependent type II interval censored data.First,we use copula function to construct the likelihood function,and then use Nelder Mead algorithm to maximize the likelihood function to get the estimation of parameters.In addition,unlike from the perspective of survival function,this paper constructs the likelihood function of interval censored data from the joint distribution function constructed by copula function.It not only gives the new derivation process of the likelihood function of two types of independent interval censored data and dependent type I interval censored data,but also gives the derivation process and expression of dependent type II interval censored data.Finally,by the simulation,we can know that the MLE obtained by using the proposed likelihood function are more accurate and more robust,which provides some theoretical support for applying the proposed likelihood function to the maximum likelihood estimation method on interval censored data.