A New Generalized Inverse Rayleigh Geometric distribution with Simulation and Applications in Medicine and Engineering

Abstract

Various limitations are inherent in existing statistical distributions as explained in literature when used in modeling the complexities of real-world data. This oftentimes brings about the development of new tractable models. This work introduces the new novel distribution named the Inverse Rayleigh Geometric (IRG) distribution. The IRG distribution boasts significant flexibility with symmetrical and asymmetrical shapes, allowing its hazard rate function to be adapted to many failure patterns experienced in various fields such as medicine, biology, and engineering. Some statistical properties of the IRG distribution, such as ordinary and incomplete moments, quantile function, stress-strength reliability, weighted moments, order statistics, information measures, and Rényi and Tsallis entropies, are studied. Simulation study was carried out to evaluate the performance of the estimation method used. The IRG distribution proves to be superior to all other models considered in this study by its ability to fit real-life data accurately. Two medical and engineering datasets are applied to demonstrate the superior fit of IRG distribution compared to competing models. The results indicate that the IRG distribution holds promise for reliability evaluations and lifetime data analysis in a variety of academic fields.