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

In this study, the distribution’s reliability and hazard functions, as well as the population parameters, are estimated for the length biased weighted Lomax (LBWLo) based on progressively Type II censored samples. The maximum likelihood and Bayesian methods are implanted to get the proposed estimators. Gamma and Jeffery's priors serve as informative and non-informative priors, respectively, from which the posterior distribution of the LBWLo distribution is constructed. To obtain the Bayesian estimates, the Metropolis-Hasting (MH) algorithm is also used. We obtain asymptotic confidence intervals based on the Fisher information matrix. Using the sample produced by the MH method, we construct the intervals with the highest posterior densities. A numerical simulation research is done to evaluate the effectiveness of the approaches. Through Monte Carlo simulation, we compare the proposed estimators 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 cases, Bayes estimates with an informative prior are more appropriate than other estimates.