A New Modification for the Inverse Rayleigh Distribution with Properties, Entropy Information, and Applications to Environmental Data

I. Elbatal; Ehab M. Almetwally; Mohammed Amine Meraou; Samirah Alzubaidi; M. H. Harpy; Elkhateeb S Aly; Rahmtalla Y. Yagoub; Abdisalan Ahmed Osman

doi:10.64389/mjs.2026.02244

Authors

I. Elbatal Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia Author
Ehab M. Almetwally Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia Author
Mohammed Amine Meraou Laboratory of Statistics and Stochastic Processes, University of Djillali Liabes, BP 89, Sidi Bel Abbes 22000, Algeria Author
Samirah Alzubaidi Department of Mathematics, Al-Qunfudah University College, Umm Al-Qura University, Mecca, Saudi Arabia Author
M. H. Harpy Department of Mathematics, Faculty of Science, Suez Canal University, Ismailia 41522, Egypt Author
Elkhateeb S Aly Department of Mathematics, College of Science, Jazan University, P.O. Box 114, Jazan 45142, Kingdom of Saudi Arabia Author
Rahmtalla Y. Yagoub Department of Statistics, Faculty of Science, University of Tabuk, Tabuk 71491, Kingdom of Saudi Arabia Author
Abdisalan Ahmed Osman 7Department of Statistics, College of Natural and Computational science, University of Kabridahar, Somali Regional State, Kebri Dehar, Ethiopia Author

DOI:

https://doi.org/10.64389/mjs.2026.02244

Keywords:

Rayleigh distribution, Application, Entropy measures, Environmental studies, Simulation

Abstract

In the present study, we develop a new version of the inverse Rayleigh model using the odd-type G family of distributions. The proposed model is highly flexible and exhibits various behaviors in terms of its density and hazard functions. We study the mathematical properties of this new model, such as moments, quantile function, moment generating function, skewness, kurtosis, and entropy measures. The unknown parameters of the proposed distribution are estimated using the well-known maximum-likelihood method. A simulation experiment is evaluated to assess the effectiveness of the applied estimation method. Finally, the superiority and flexibility of the newly presented distribution are examined by analyzing two real data sets. The application of the proposed model is compared with other existing probability distributions, and based on specific evaluation criteria, we observe that the proposed distribution offers optimal fitting compared to other rival distributions.