Estimation for Inverse Burr Distribution under Generalized Progressive Hybrid Censored data with an application to Wastewater Engineering Data

Abstract

The inverse Burr distribution is a significant and commonly used lifetime distribution, which plays an important role in reliability engineering. In this article, the estimation of parameters of the inverse Burr distribution based on generalized Type II progressive hybrid censored sample is studied. The expectation-maximization (EM) algorithm is employed for computing the maximum likelihood estimates of the unknown parameters. It is shown that the maximum likelihood estimates exist uniquely. The asymptotic confidence intervals for the parameters are constructed using the missing value principle. Under Bayesian framework, the Bayes estimators are developed based on Lindley's technique and Metropolis-Hastings algorithm. Furthermore, the highest posterior density (HPD) credible intervals are successively constructed. Finally, simulation experiments are implemented to access performance of several proposed methods in this article, and sewer invert trap real data is presented to exemplify the theoretical outcomes.

Keywords

• Bayes estimators
• EM algorithm
• Generalized Type II progressive hybrid censoring
• HPD credible interval
• Inverse Burr distribution
• Separation of sewer solids