The Study Of Bayes Estimation Problems Of Lifetime Distribution

Bayes estimation is a method to estimate the total parameter synthesizing totalityinformation, sample information and prior information roundly. And it plays animportant role in the product lifetime estimation. Rayleigh Distribution andTwo-Parameter Exponential Weibull Distribution are significant life distributions.Now there’re many articles about the parameter estimation of life distributions, butmost of them estimate contraposing only one parameter. What’s more, Zero-FailureData is a hot spot. Therefore, this essay will make a study aimed at the questionsabove and mainly discuss the following several aspects:Firstly, in the case of complete sample, we will discuss the inverse parameter ofRayleigh distribution under the weighed p,q entropy loss function in the respect of themaximum likelihood estimation, Bayes estimation, admissibility and the lowerconfidence limit.Secondly, in the case of type-Ⅱ doubly censored scheme, we will discuss theBayes estimation of inverse parameter of Rayleigh distribution under the Linex lossfunction.Thirdly, in the case of progressively type-Ⅱ censored samples, weconsider theestimation of two-parameter Exponential Weibull distribution when the twoparameters are unknown under the weighed p,q entropy loss function. And get theanalythical form of Bayesian estimate using Lindley approximate. And we verify therationality of the result making use of Matlab.Fourthly, we discuss the Bayes estimation and multilayer Bayes estimation of thefailure probability in the case of zero-failure data and prove that they’re of equal valuegradually.