Estimations of Modified Lindley Parameters Using Progressive Type-II Censoring with Applications

This study addresses the estimation problems of the modified Lindley distribution using a progressive Type-II censoring plan. Using the maximum likelihood and maximum product of spacing and Bayesian estimation methods, the unknown parameter, reliability, and hazard rate functions are estimated. Employing the assumption of the gamma prior and a symmetric loss function, Bayes estimators are investigated when the observed data are obtained using the likelihood and product of spacing functions. Additionally, the approximate confidence intervals using both classical methods and the highest posterior density credible intervals are also discussed. To assess the different estimating strategies, a comprehensive simulation experiment that considers various sample sizes and censoring schemes is implemented. Finally, two actual data sets are examined to verify the utility of the modified Lindley distribution and the usefulness of the suggested estimators. The findings demonstrate that, in order to obtain the necessary estimators, the maximum product of the spacing method is preferred over the maximum likelihood method; whereas, when compared to the conventional techniques, the Bayesian approach using the likelihood and product of spacing functions provides more acceptable estimates.