Different Estimation Methods and Joint Condence Region for the Inverse Burr Distribution Based on Progressively First-Failure Censored Sample with Application to the Nanodroplet Data

In this article, the point and interval estimation of parameters for an in-verse Burr distribution based on progressively rst-failure censored sampleis studied. In point estimation, the maximum likelihood and Bayesian meth-ods are developed for estimating the unknown parameters. An expectation-maximization algorithm is applied for computing the maximum likelihoodestimators. The Bayes estimates relative to both the symmetric and asym-metric loss functions are provided using the Lindley's approximation andthe Metropolis-Hastings algorithm. In interval estimation, approximate andexact condence intervals with the exact condence region for the two parameters have been introduced. Moreover, the proposed methods are carriedout to a real data set contains the spreading of nanodroplet impingementonto a solid surface in order to demonstrate the applicabilities.

本文针对基于逐步首失效截尾样本（progressively first-failure censored sample）的逆Burr分布（Inverse Burr Distribution）的参数点估计与区间估计展开研究。在点估计环节，本文针对模型未知参数构建了极大似然估计与贝叶斯估计两类方法：采用期望-最大化（Expectation-Maximization）算法求解极大似然估计量；针对对称与非对称损失函数，分别通过林德利（Lindley）近似法与梅特罗波利斯-黑斯廷斯（Metropolis-Hastings）算法推导得到对应的贝叶斯估计结果。在区间估计环节，本文针对模型的两个参数提出了近似置信区间、精确置信区间以及精确置信域。此外，本文采用包含纳米液滴撞击固体表面铺展过程的真实数据集，对所提方法的适用性进行了验证。