Bayesian and Frequentist Estimation of the Entropy for the Symmetric Double Pareto Distribution Using Random Sampling

Entropy is a useful measure in several fields; therefore, estimation of entropy has a wide range of applications. This research aims to estimate the entropy of the symmetric double Pareto (SDP) distribution under different sampling schemes, namely: simple random sampling, ranked set sampling, double ranked sampling, and systematic ranked set sampling. We adopt both maximum likelihood and Bayesian estimation methods. To deal with the fact that the support of the SDP distribution depends on its parameter, a highly efficient Bayesian approach is proposed and implemented through Markov Chain Monte Carlo methods. Both point and interval estimation are studied. The proposed Bayesian method is compared with maximum likelihood and bootstrapping methods. A comprehensive simulation study is conducted and the performance of the proposed estimation methods is studied through the mean square error and coverage probability. It was observed that the proposed Bayesian method outperforms the maximum likelihood and bootstrapping methods for small and moderate sample sizes. The discussed methods have similar performance for larger sample sizes. In terms of the sampling schemes, it was observed that the DRSS is the best for small <img src=image/13441419_01.gif>, while SRSS has better performance as <img src=image/13441419_01.gif> increases. The results were confirmed by applying the proposed methods to a real data example.