Piriaei Hassan, Yari Gholamhossein, Farnoosh Rahman
Department of Statistics, Science and Research Branch, Islamic Azad University, Tehran, Iran.
School of mathematics, University of Science and Technology, Tehran, Iran.
J Appl Stat. 2019 Sep 11;47(5):865-889. doi: 10.1080/02664763.2019.1661359. eCollection 2020.
Estimation of reliability and hazard rate is necessary in many applications. To this aim, different methods of estimation have been employed. Each method suffers from its own problems such as complexity of calculations, high risk and so on. Toward this end, this study employed a new method, E-Bayesian, for estimating the parametric functions of the Generalized Inverted Exponential distribution, which is one of the most noticeable distributions in lifetime studies. Relations are derived under a squared error loss function, type-II censoring and a conjugate prior. E-Bayesian estimations are obtained based on different priors of the hyperparameters to investigate the influence of different prior distributions on these estimations. The asymptotic behaviors of E-Bayesian estimations and relations among them have been investigated. Finally, a comparison among the maximum likelihood, Bayes and E-Bayesian estimations in different sample sizes are made, using a real data and the Monte Carlo simulation. Simulations show that the new presented method is more efficient than previous methods and is also easy to operate. Also, some comparisons among the results of Generalized Inverted Exponential distribution, Exponential distribution and Generalized Exponential distribution are provided.
在许多应用中，估计可靠性和故障率是必要的。为此，人们采用了不同的估计方法。每种方法都有其自身的问题，如计算复杂性、高风险等。为此，本研究采用了一种新的方法——经验贝叶斯方法，用于估计广义倒指数分布的参数函数，该分布是寿命研究中最显著的分布之一。在平方误差损失函数、II型删失和共轭先验的条件下推导了相关关系。基于超参数的不同先验得到经验贝叶斯估计，以研究不同先验分布对这些估计的影响。研究了经验贝叶斯估计的渐近行为及其之间的关系。最后，使用实际数据和蒙特卡罗模拟，对不同样本量下的最大似然估计、贝叶斯估计和经验贝叶斯估计进行了比较。模拟结果表明，新提出的方法比以前的方法更有效，且易于操作。此外，还对广义倒指数分布、指数分布和广义指数分布的结果进行了一些比较。
