Estimation of reliability and hazard rate is one of the most important problems raised in many applications especially in engineering studies as well as human lifetime. In this regard, different methods of estimation have been used. Each method exploits various tools and suffers from problems such as complexity of computations, low precision, and so forth. This study is employed the E-Bayesian method, for estimating the parameter and survival functions of the Weibull Generalized Exponential distribution. The estimators are obtained under squared error and LINEX loss functions under progressive type-II censored samples. E-Bayesian estimations are derived based on three priors of hyperparameters to investigate the influence of different priors on estimations. The asymptotic behaviours of E-Bayesian estimations have been investigated as well as relationships among them. Finally, a comparison among the maximum likelihood, Bayes, and E-Bayesian estimations are made, using real data and Monte Carlo simulation. Results show that the new method is more efficient than previous methods.
翻译：估计可靠性和危险率是许多应用,特别是工程研究和人类寿命期应用中出现的最重要问题之一。在这方面,采用了不同的估计方法。每种方法都利用了各种工具,并遇到各种问题,例如计算的复杂性、低精确度等等。本研究采用了E-Bayesian方法,以估计Weibull通用指数分布的参数和生存功能。估计数据是在正方形错误和累进型二类检查样品LINEX损失功能下取得的。E-Bayesian估计数据基于前三次超光度计得出,以调查不同前几次对估计的影响。E-Bayes估计的无效果行为以及它们之间的关系都得到了调查。最后,利用真实数据和蒙特卡洛模拟,对Bayes和E-Bayesian的估计进行了最大可能性的比较。结果显示,新方法比以前的方法更有效率。
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