Modeling Physical and Medical Lifetime Data Using the Inverse Power Entropy Chen Distribution

Dina A. Rammadan (), Ahmed Mohamed El Gazar, Mustafa M. Hasaballah, Oluwafemi Samson Balogun, Mahmoud E. Bakr and Arwa M. Alshangiti
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Dina A. Rammadan: Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 33516, Egypt
Ahmed Mohamed El Gazar: Department of Basic Sciences, Higher Institute for Commercial Sciences, Almahlla Alkubra 31951, Egypt
Mustafa M. Hasaballah: Department of Basic Sciences, Marg Higher Institute of Engineering and Modern Technology, Cairo 11721, Egypt
Oluwafemi Samson Balogun: Department of Computing, University of Eastern Finland, FI-70211 Kuopio, Finland
Mahmoud E. Bakr: Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
Arwa M. Alshangiti: Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Mathematics, 2025, vol. 13, issue 23, 1-37

Abstract: This paper presents a new model that surpasses traditional distributions, specifically the three-parameter distribution of the Inverse Power Entropy Chen (IPEC) model. In comparison to the existing distributions, the latest one presents an exceptionally diverse array of probability functions. The density and hazard rate functions have characteristics indicating that the model is adaptable to many types of data. The study explores the mathematical features of the IPEC distribution, including moments with some related measures, quantile function, Rényi entropy, Tsallis entropy, and order statistics. To estimate the parameters of the IPEC model, we utilized seven classical estimation strategies, including maximum likelihood estimators, Anderson–Darling estimators, right-tail Anderson–Darling estimators, Cramér–von Mises estimators, percentile estimators, least-squares estimators, and weighted least-squares estimators. To evaluate the efficacy of these estimating approaches across varying sample sizes, Monte Carlo simulations are performed. The efficacy of each estimator is evaluated through comparisons of average relative bias and mean squared error, highlighting their suitability for the used samples. Three applications utilize real-world datasets related to medical and physical fields, demonstrating the usefulness of the new model in relation to several established competitive models. This empirical investigation further supports the utility and adaptability of the inverse power entropy Chen model in capturing the intricacies of distinct datasets, hence delivering useful insights for practitioners in numerous domains.

Keywords: entropy chen distribution; probability weighted moments; least squares estimation method; order statistics; real datasets (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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