熵损失函数下广义指数分布的可靠性估计

在广义指数分布场合下, 讨论了其参数、可靠性指标的估计及性质. 基于熵损失函数, 在共轭先验分布下, 通过对分布函数进行变换, 获得了该分布参数、可靠性指标的 UMVUE、最小风险同变估计、Bayes 估计和经验 Bayes 估计, 并证明了形如 cT(x) + d]^-1 的一类估计的容许性. 最后运用 Monte-Carlo 方法对各种估计的 MSE 进行了模拟比较. 结果表明, 经验贝叶斯估计精度较高.

Reliability estimations of generalized exponential distribution under entropy loss function

In generalized exponential distribution, the estimations and their admissibility of the parameter and the reliability index of generalized exponential distribution are discussed. The UMVUE MRE Bayesian estimation and empirical bayes estimation for parameter and reliability index of the generalized exponential distribution are obtained used conjugate prior under entropy loss function by transforming the distribution function. And we prove the estimation of the generalized exponential distribution with the form of cT(x) + d]^-1 is admissibility. At last, the MSE of the estimations are compared based on Monte Carlo simulation study. According to these comparisons, it is suggested that the empirical Bayes estimation have high-precision.