Bayesian Estimation of the Entropy of the Half-Logistic Distribution Based on Type-II Censored Samples

This paper estimates the entropy of the half-logistic distribution with the scale parameter based on Type-II censored samples. The maximum likelihood estimator and the approximate confidence interval are derived for entropy. For Bayesian inferences, a hierarchical Bayesian estimation method is developed using the hierarchical structure of the gamma prior distribution which induces a noninformative prior. The random-walk Metropolis algorithm is employed to generate Markov chain Monte Carlo samples from the posterior distribution of entropy. The proposed estimation methods are compared through Monte Carlo simulations for various Type-II censoring schemes. Finally, real data are analyzed for illustration purposes.