In this study, we study the empirical Bayes estimation of the parameter of the exponential distribution. In the empirical Bayes procedure, we employ the non-parameter polynomial density estimator to the estimation of the unknown marginal probability density function, instead of estimating the unknown prior probability density function of the parameter. Empirical Bayes estimators are derived for the parameter of the exponential distribution under squared error and LINEX loss functions. We use numerical examples to compare the empirical Bayes estimators we obtained under squared error and LINEX loss functions and we get the result of the mean square error of the empirical Bayes estimator under LINEX loss is usually smaller than the estimator under squared error loss function, so it is more better.

In this paper, we consider one-parameter exponential family and obtain the Bayes and. empirical Bayes estimators of the unknown parameter based on record values under a precaution asymmetry entropy loss function. The admissibility and inadmissibility of a class of inverse linear estimators of are studied based on upper records.

Loss function is an important content in Bayes statistical inference. The task of this article is to study the reliability analysis of the exponential model based on a new proposed symmetric loss function. The new proposed loss function is established on the basis of the LINEX asymmetric loss function. Firstly, the Bayes estimation of the parameter is derived under the prior distribution of the parameter based on non-information Quasi prior distribution, and then the admissibility of the estimators are also discussed. Furthermore, this paper puts forward a novel testing procedure to evaluate the lifetime performance of exponential products based on the new derived Bayes estimator. Finally, Monte Carlo statistical simulation and an applicable example are used to illustrate that the new proposed Bayes estimators and testing procedure are effective and feasible.

No abstract

No abstract