Abstract

In this article, we consider estimating the parameters, reliability function R(t) and failure rate function H(t) of the two-parameter bathtub-shaped distribution introduced by Chen (2000 Chen, Z. 2000. A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function. Statistics & Probability Letters 49 (2):155–61.[Crossref], [Web of Science ®] , [Google Scholar]) based on the progressive first-failure censored sample. The maximum likelihood estimators and Bayes estimators under squared error loss function are derived. We obtain the asymptotic confidence intervals for the parameters using the observed Fisher information matrix. The parametric bootstrap confidence intervals of reliability characteristics are also proposed. Lindley approximation procedure is adopted to establish Bayes estimates. Furthermore, we conduct Monte Carlo simulation to compare the behaviors of different methods. A real data set is analyzed to illustrate the proposed methods.

摘要

在本文中，我们考虑估计Chen ( 2000 ) 引入的双参数浴缸形分布的参数、可靠性函数R ( t ) 和故障率函数H ( t ) 陈，Z. 2000 . 一种新的具有浴缸形状或增加故障率函数的两参数寿命分布。统计与概率快报49 (2): 155 – 61。[交叉引用]、[Web of Science ®]  、[谷歌学术]) 基于渐进式第一次失败删失样本。推导出平方误差损失函数下的最大似然估计量和贝叶斯估计量。我们使用观察到的 Fisher 信息矩阵获得参数的渐近置信区间。还提出了可靠性特性的参数引导置信区间。采用 Lindley 近似程序来建立贝叶斯估计。此外，我们进行蒙特卡罗模拟来比较不同方法的行为。分析一个真实的数据集来说明所提出的方法。