Parameter Estimation Of Exponential Distribution From Incomplete Data

Data processing is one of the most important means of scientific and social research as well as an indispensable link in the statistical work.Usually we will meet incomplete data while dealing with the data because of varieties of reasons,such as the requirement of economy and time and the errors made during the process of data survey and storing.The data can't be analysed by traditional method and the outlier data will also affect the sample,which will disturb people's judgement and decisions,and finally,lead to a lot of economic loss.Therefore,people need to process data in a particular way to extract useful information and reduce the effect of outlier data.This paper analyses the estimate of parameter of exponential distribution,which is the most basic and common distribution in reliability statistics in incomplete data.The main idea concludes these following two aspects.First,introduce the MLE of parameter ? of exponential distribution in fixed number truncated test.Considering the data request of fixed number truncated test will not be matched sometimes,the nature of order statistics of exponential distribution is studied and a class of unbiased estimators of parameter ? is built.This method can be used in the condition of any number of order statistics and perform well in missing data occasion.Comparing with the MLE of parameter ? of exponential distribution in fixed number truncated test and come to the conclusion that the MLE is a special case of these unbiased estimators built by this method.The second,research the confidence interval for parameter of exponential distribution from incomplete data.First,build the pivot Z with median and another quantile of the sample.Then,deduce the accurate probability density function of Z,which will help to calculate the confidence interval of parameter ?.Finally,give the asymptotic distribution of the pivot Z and the approximate confidence interval for parameter ?.