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

Abstract Numerous probability distributions are utilized to predict and model real-world phenomena across diverse applied domains, including reliability engineering, environmental studies, medical sciences, economics , actuarial science, finance, and insurance. However, the authors have developed no flexible probability distribution in the literature that accommodates every phenomenon because phenomena are complex. In the present study, we develop a new version of the inverse Rayleigh model using the new odd type-G family of distributions. The proposed model is very flexible and offers different 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 estimation technique. 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 made with the other existing probability distributions, and based on certain evaluation criteria, we observe that the proposed distribution offers optimal fitting compared to other rival distributions.