Bayesian Statistical Inference Of Exponential Distribution Under The Condition Of 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 random phenomenon, it comes to a random inference problem that we try to determine the reliability indexes of the production. In the process of reliable experimentation, the exponential distribution is very abroad of applications. hence it is a very significant research of applying Bayes experience,Bayes theory and the way of Bayes identification to a reliable field. Basing on the fruit of the predecessors, this paper makes some researches on the above-mentioned question, the main works including.First, it gives parameters with the signal parameter exponential distribution of Bayes estimate in the lapse case and reliable experience Bayes estimate. At the same time, in the experiment of type-I censoring, it gives rule of minimum posterior risk to exponential distribution with signal parameter, and the way of Bayes differentiate.This paper introduces the statistical inference for the exponential distribution with two parameter under type-I censoring. And the point estimation and interval estimation under multiply type-I censoring is given out.Secondly, the empirical Bayes (EB) test problem of parameter for scale exponential family under Linex loss function has been discussed. The EB test rules are constructed by kernel estimation method. The asymptotically optimality and convergence rates of EB test rules are obtained. Finally, applications of the main results are shown.At last, the distribution of exponential is studied in the situation of zero-failure data. This paper discusses by the Bayesian methods zero-failure reliability demonstration testing procedure for the exponential distribution with two parameter and single parameter. And give the Bayesian estimation of pi , then calculation is performed regarding to practical problem.