Statistical Inference Research For Censored Data

With the industrial manufacturing technology becoming more and more mature,the quality of products has been greatly improved.In the lifetime experiment of products,since the cost and time of experiment are limited,the high-quality products are usually collected in the form of censored lifetime.Commonly,censored data include traditional type-I censored data,type-II censored data and progressive censored data.In addition,there are hybrid type-I censored data,hybrid type-II censored data and progressive hybrid censored data,which are obtained under more flexible experiments.In view of the high practicability of censored data in the fields of medicine,finance,survival analysis,reliability analysis and so on,this paper makes statistical analysis on such data by using different inference methods.The specific research contents are as follows:(1)The statistical inference of the inverted exponentiated Rayleigh model is studied.Based on the modified progressive hybrid censored data,the maximum likelihood estimates and approximate confidence intervals of model parameters are established,and the existence and uniqueness of the maximum likelihood estimates are guaranteed.As a supplement to the likelihood method,a generalized estimation method and corresponding generalized sampling algorithm are proposed based on pivotal quantities as well.In addition,for the censored samples,the corresponding lifetime prediction problem is discussed.Finally,numerical simulation studies are carried out to evaluate the effects of the proposed methods.The results indicate that both estimation methods perform well,but in general,the performance of generalized estimation is better than that of traditional likelihood estimation.(2)The statistical inference of left truncated and right censored dependent competing risk data is studied.When the latent lifetime is distributed by Marshall–Olkin bivariate Rayleigh distribution,the maximum likelihood estimates of unknown parameters are established,and corresponding approximate confidence intervals are constructed by using a Fisher information matrix and asymptotic approximate theory.Furthermore,Bayesian estimates and associated high posterior density credible intervals of unknown parameters are provided based on certain prior information.At the same time,when there is an order restriction between model parameters,the point and interval estimates based on likelihood and Bayesian methods are discussed respectively.Besides,the lifetime prediction issue of censored samples is also discussed based on likelihood and Bayesian methods respectively.The numerical simulation results show that when the prior information is sufficient,the effect of Bayesian estimation is better than that of maximum likelihood estimate.