Some Inference Problems Research Under The General Type-II Progressive Censoring Sample

Statistical analysis of life time data is an attractive subject in Medical, Biology and en-gineering.In 1950s,in order to improve the reliability of the products,statisticians engaged in working on different type of life time data,which maked the theory ,method and applications of the analysis on it developed quickly . The general Type- II progressive censoring applied frequently is an important way for getting the data. For getting the information of the research object, it is necessary to do some inferences under general Type- II progressive censoring sample.This paper firstly gives some properities of the order statistics under general Type- II progressive censoring (r≠ 0),including explicit marginal and joint function of the order statistics and the single or product moments of the order statistics under this censoring. The third chapter use EM algorithm to determine the maximamum likelihood estimates when the likelihood equation do not provide explicit solutions based on the general Type- II progressive censoring sample. The asympotic variance-covariance matrix of the MLEs are computed by means of missing information principle".This methodology is illustrated with two popular parameter models in lifetime analysis from weibull and lognormal distribution, the EM algorithm yield the same values as the newton-raphson result in and simulated values are presented in the paper. The optimal censoring plan can be determined from these values under two wellknown optimality criteria and it is "naturally robust." For the lognormal sample,an approximate method is used to develop estimates which are explicit and are as efficient as the MLEs from the newton-raphson algorithm .In Chapter 5,Use the logarithmic derivative formula of Г function, analysis the characters of t distribution density function in detail, and the effects of change of the parameter n on density curve. Points out the properties of maximum value of t distributed density function, and the relation of different t distributed density function according to different parameters n.