The Marshall-Olkin Inverse Rayleigh Distribution and Its Applications

The Marshall-Olkin Inverse Rayleigh (MOIR) distribution is an extension of the classical Inverse Rayleigh distribution, incorporating Marshall-Olkin shock model that enhances its flexibility and applicability in various fields. This paper presents the derivation of the MOIR distribution and explores its fundamental properties, including moments, reliability measures, and order statistic. Expression for the mean, variance, skewness and kurtosis are also presented. Parameter estimation is addressed through maximum likelihood method, demonstrating its applicability and efficiency through simulation studies. Furthermore, we illustrate the practical utility of the MOIR distribution in modeling real-world data. The results highlight the flexibility and robustness of the MOIR distribution in capturing diverse patterns in lifetime data, offering a valuable tool for statisticians and practitioners in various fields.