Abstract

The issue of this paper is the inference about the parameters of modified extended exponential distribution (MExED) planned on the progressively type-II censored (Prog -II- C) samples. The maximum likelihood and Bayesian estimates are procured for the parameters of MExED. Approximate confidence intervals (ACIs), the reliability and risk functions are estimated based on the asymptotic distribution of maximum likelihood estimates (MLEs) and delta method approach. Moreover, Bayesian estimates are obtained for symmetric and asymmetric loss functions such as squared error loss (SEL) and LINEX loss functions. Gibbs within Metropolis–Hasting samplers procedure is applied for using the Markov chain Monte Carlo (MCMC) technique to get on the Bayes estimates of the unknown parameters and their credible intervals (CRIs). Finally, a real-life data set, which represents the breakdown of some mechanical components, is considered an application of the proposed methods.

摘要

本文的问题是对计划在渐进式 II 型删失 (Prog -II- C) 样本上的修正扩展指数分布 (MExED) 参数的推断。为 MExED 的参数获得最大似然和贝叶斯估计。近似置信区间 (ACI)、可靠性和风险函数是根据最大似然估计 (MLE) 的渐近分布和增量法方法估算的。此外，还获得了对称和非对称损失函数的贝叶斯估计，例如平方误差损失 (SEL) 和 LINEX 损失函数。Metropolis–Hasting 抽样程序中的 Gibbs 应用于使用马尔可夫链蒙特卡罗 (MCMC) 技术来获得未知参数及其可信区间 (CRI) 的贝叶斯估计。最后，一个真实的数据集，