On survival estimation of Lomax distribution under adaptive progressive type-II censoring

The main objective of the research described in the article is to study the maximum likelihood (ML) estimation and the Bayesian approach for parameter estimation of the Lomax distribution. Additionally, the study aims to determine the approximate intervals for the parameters and the survival function based on adaptive progressive type-II censored data. The ML estimators of the probability distribution's parameters were calculated using the Newton-Raphson method, while the delta method was utilised to compute the approximate confidence intervals for the survival function. The Bayesian approach was also used to estimate the unknown parameters and survival function. This was achieved through the construction of Bayesian estimators under an informative and non-informative prior based on the squared error loss function (SELF) and approximate credible intervals. The Markov Chain Monte Carlo (MCMC) method was employed for this purpose. A Monte Carlo analysis was conducted to test the efficiency of the proposed method in various situations based on different criteria such as mean-squared error, bias, coverage probability, and expected length-estimated criteria. The results indicate that the Bayesian approach out-performs the likelihood method in estimating the Lomax model parameters. Finally, the study includes an application of these methods to real data.