Journals Information
Mathematics and Statistics Vol. 13(6), pp. 498 - 510
DOI: 10.13189/ms.2025.130606
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Bayesian and Frequentist Estimation of the Entropy for the Symmetric Double Pareto Distribution Using Random Sampling
Mohammed Obeidat *, Farah Telfah , Mariam Setaboha , Mohammad Al-Talib
Department of Statistics, College of Science, Yarmouk University, Irbid, Jordan
ABSTRACT
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 
, while SRSS has better performance as increases. The results were confirmed by applying the proposed methods to a real data example.
KEYWORDS
Bayesian Estimation, Differential Entropy, Double Ranked Set Sampling, Linex Loss Function, Markov Chain Monte Carlo, Maximum Likelihood Estimation, Ranked Set Sampling, Symmetric Double Pareto Distribution, Systematic Ranked Set Sampling
Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Mohammed Obeidat , Farah Telfah , Mariam Setaboha , Mohammad Al-Talib , "Bayesian and Frequentist Estimation of the Entropy for the Symmetric Double Pareto Distribution Using Random Sampling," Mathematics and Statistics, Vol. 13, No. 6, pp. 498 - 510, 2025. DOI: 10.13189/ms.2025.130606.
(b). APA Format:
Mohammed Obeidat , Farah Telfah , Mariam Setaboha , Mohammad Al-Talib (2025). Bayesian and Frequentist Estimation of the Entropy for the Symmetric Double Pareto Distribution Using Random Sampling. Mathematics and Statistics, 13(6), 498 - 510. DOI: 10.13189/ms.2025.130606.