E-Bayesian estimation and hierarchical Bayesian estimation of failure rate

Abstract

a b s t r a c tThis paper introduces a new method, E-Bayesian estimation method, to estimate failure rate. The method is suitable for the censored or truncated data with small sample sizes and high reliability. The definition and properties of E-Bayesian estimation are given. A real data set is discussed, which shows that the method is both efficiency and easy to operate.

E-Bayesian estimation for the geometric model based on record statistics

“…According to Han [16], the prior parameters α and β should be selected to guarantee that f (θ|α, β) is a decreasing function of θ. The derivative of f (θ|α, β) with respect to θ is…”

E-Bayesian Estimation Based On Generalized Half Logistic Progressive Type-II Censored Data

“…This paper introduces a new method, called E-Bayesian estimation(see Han [6]), to estimate parameter and reliability function of Generalized Half Logistic distribution when progressive Type II censoring is performed. Based on the results shown in Table-1, one can conclude, Generally, the MSE of the E-Bayesian estimates of β are the smallest MSE as the as compared with the Bayesian estimates.…”

E-Bayesian analysis of the Gumbel type-ii distribution under type-ii censored scheme

“…EBMi i   Lemma 5: It follows from (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19), (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20) and (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21) …”

“…We considered different sample sizes c  for these cases, we genera for e from the uniform priors distributions (0, 1) and (0, c) respectively given in (3-4), (3)(4)(5) and (3)(4)(5)(6). , (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19), (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20) and (3-21) respectively. We repeated this process 10000 times and compute the Mean Square Error (MSE) for the estimates for different censoring schemes (different values of , nr) and given values of ,, cs where and  stands for an estimator of  .…”