Classical and Bayesian Inference for the Length Biased Weighted Lomax Distribution under Progressive Censoring Scheme

Year 2024, , 979 - 1002, 01.06.2024

Amal S. Hassan , Samah A. Atia , Hiba Z. Muhammed

https://doi.org/10.35378/gujs.1249968

Abstract

In this study, the length biassed weighted Lomax (LBWLo) distribution's reliability and hazard functions, as well as the population characteristics, are evaluated using progressively Type II censored samples. The proposed estimators are obtained by combining the maximum likelihood and Bayesian approaches. The posterior distribution of the LBWLo distribution is derived from the Gamma and Jeffery's priors, which, respectively, act as informative and non-informative priors. The Metropolis-Hasting (MH) algorithm is also utilized to get the Bayesian estimates. Based on the Fisher information matrix, we derive asymptotic confidence intervals. We create the intervals with the highest posterior density using the sample the MH technique generated. Numerical simulation research is done to evaluate the effectiveness of the approaches. Through Monte Carlo simulation, we compare the proposed estimates in terms of mean squared error. It is possible to get coverage probability and average interval lengths of 95%. The study's findings supported the idea that, in the majority of the cases, Bayes estimates with an informative prior are more appropriate than other estimates. Additionally, one set of actual data supported the findings of the study.

Keywords

Length biased weighted Lomax, Maximum likelihood estimation, squared error loss function, informative prior, Markov Chain Monte Carlo

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