Moment Estimation And Hypothesis Testing Of Exponential Distribution Under Interval Censored Samples

In many branches of science ,such as medicine ,biology, insurance, reliability engineering project science ,public hygiene, economics , demographics etc , problems of estimating and forecasting the time of certain events occur exist . From the obtained data ,these data have a common characteristic that the results of surveying are either censored or truncated . Especially we call it interval-censored when we only know the event happens in certain time area. When interval censoring arises, almost all traditional statistical methods can(?)work any more.There is an enormous amount of literature on the interval censored data. In these studies , nonparametric likelihood estimation(NPMLE) are widely used; but Its limitation is that it is complicated to work out the functions and in most situations we can only use iterative operations to get an approximate solution . In this paper, I will use unbiased transformation method to solve some estimating and hypothesizing problems of interval censored data . Based on the observations we construct a series of new variables to substitute the censored variable. These new variables have the same expectation as the censored variable.Suggested by the idea of Class-K method , I have mainly done three tasks: First , we studied the two moment estimating problem for the exponential distributionbased on the interval censored data. Bothδ_i and (V_i,δ_i) are used to constructedsample moment ;Second, we studied the one side hypothesis testing problem for the average life of exponential distribution based on the interval censored data t; In the third section, we consider the model ranked testing problem based on the interval censored data.