Parameter Estimation Of Weibull Distribution With Double B-p Method For Type-? Censored Data

The research of lifetime data is important for survival analysis and reliability analysis,and the two-parameter Weibull distribution is well used for portraying and modeling of lifetime data.However,researchers often terminate the test as a certain amount of lifetime data has being observed in survival analysis or lifetime-testing experiments due to the limits of time,resources or budget on data collection,so as to obtain the named type II censored data.For incomplete data,Weibull distribution has shown good adaptability and provided reliable life analysis and prediction.Therefore,parameter estimation for the two parameter Weibull distribution based on type II censored data is of great significance.This thesis considers the parameter estimation of two parameter Weibull distribution for type II censored data with small samples.Firstly,the EM algorithm is employed to estimate the parameters of the two parameter Weibull distribution under type II right censoring,and the properties of the method are discussed.In addition,this method is compared with the well used maximum likelihood estimation based on Newton iteration.Secondly,we propose the Double B-P method to estimate the confidence interval of the two parameter Weibull distribution.The methods of calculating the Weibull parameter confidence intervals based on type II right censoring including the Wald method,profile likelihood method and bootstrap method in the existing studies.However,the Wald method has a high accuracy only in the case of large samples,and the confidence interval is not accurate in the case of small samples.The profile likelihood method obtains the approximate solution of the parameter but requires too much iterations.The boostrap method can obtain a relatively narrow confidence interval,as the censoring rate over 30%,the estimation of the interval is not accurate.This thesis discusses the Double B-P method for interval estimation,which reduce the expected error of the boostrap sampling by carrying out the further sample from the boostrap samples.Finally,this thesis uses numerical simulation and empirical analysis to verify the feasibility of the Double B-P method.