Research On The Algorithm Of The Maximum Likelihood Estimation Based On Complicated Censoring Data

With the development of society and further understanding of the issue, censored data arise in many research areas, such as bio-medical science, insurance actuarial science, economic and so on. And the study of simple censoring mechanism often can not meet the realistic problems, so the statistical inference of the complex censored data has gradually become the focus of study and the corresponding research has been widely applied in many fields.This paper introduces the types and the present situation of the complex censored data, the advantages and disadvantages of the different types of the censored data (adaptive progressive type-Ⅱ hybrid censoring, progressive type-Ⅰ interval censoring) and the model setups. The adaptive progressive type-Ⅱ hybrid censored mechanism is widely applied in the field of reliability research; progressive type-Ⅰ interval censoring mechanism is widely used in clinical medicine and engineering fields.This paper mainly discusses the problem of maximum likelihood estimation algorithm based on the complex censoring mechanisms. The article has the following components.The first chapter introduces the research practical significance and the general development situation of the parameter estimation based on the complex censoring data. The second chapter introduces several common complex censored mechanisms and life model, meanwhile, gives the traditional parameter estimation method, the maximum likelihood estimation (MLE). The third chapter considers the MLEs of the Weibull distribution based on adaptive progressive type-Ⅱ hybrid censoring mechanism and at the same time gives the bootstrap correct biased estimation when the sample is small.The fourth chapter considers the parameter estimation of the mixed generalized exponential distribution based on adaptive progressive type-Ⅱ hybrid censoring mechanism. Here, the maximum likelihood estimation has no analytical form, so the application of EM iterative algorithm is given to parameter estimation. The fifth chapter discusses the MLEs of the mixed generalized exponential distribution based on progressive type-Ⅰ interval censoring and considers the EM algorithm to solve the problem and applies the algorithm to a set of real medical data.