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

Abstract

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.