Estimation of Entropy for Log-Logistic Distribution under Progressive Type II Censoring

Abstract

Entropy is a useful indicator of information content that has been used in a number of applications. The Log-Logistic (LL) distribution is a probability distribution that is often employed in survival analysis. This paper addresses the problem of estimating multiple entropy metrics for an LL distribution using progressive type II censoring. We derive formulas for six different types of entropy measurements. To obtain the estimators of the proposed entropy measures, the maximum likelihood approach is applied. Approximate confidence intervals are calculated for the entropy metrics under discussion. A numerical evaluation is performed using various censoring methods and sample sizes to characterize the behavior of estimator’s measures using relative biases, related mean squared errors, average interval lengths, and coverage probabilities. Numerical analysis revealed that the accuracy measures improve with sample size, and the suggested entropy estimates approach the genuine values as censoring levels decrease. Finally, an actual dataset was evaluated for demonstration purposes.