Statistical Inference Of Two-parameter Exponential Distribution Under The Condition Of Multiply Type-II Censoring

With the development of science and technology, the people attach more and more importance to the reliability of production. Because the life of the production is a stochastic phenomenon, it comes to a statistical inference problem that we try to determine the reliability indexes of the production. In order to make clear the life distribution of the production, measured and solved the indexes of reliability and study the invalid mechanism of the production to give some pieces of advice about improving the reliability of the production, we often have to make the life experiment. The life experiment is separated into two kinds: complete life experiment and"cutting tail"experiment, often the later one is used widely.When we deal with the practical problem by the statistical methods, we often encounter the trouble about missing data. For example, during the experiment on the life of production, some data of experiment are missed or unobserved owing to the equipment of experiment and observation means or other difficulties. So we get"missing data". It is not worth and unable to make the experiment again as the result of the parts of missing data.It is special and more difficult question how to analyze statistically about the existing data after"missing data". So it is becoming a new and important field on the reliability analysis how to research a scientific and effective statistical analysis to deal with the incomplete data under the condition of missing data.Under the condition of multiple type-II censoring, the likehood function so complex that it is hardly to get the estimate of the parameters. First of all, this paper gets the approximate maximum likehood estimate of two-parameter exponential distribution, using the mid-value theorem, and discusses the difference between this estimate and the accurate maximum likehood estimate. Then, the paper gives an iterative equation of the Bayes estimate, the convergence condition of this iterative equation and the convergence rate of the Bayes estimates according to the number of the samples (n) are also given. Finally ,it is showed the precision of the Bayes estimate is better than the approximate maximum likehood estimate by the simulation results.