Extension Odd Generalized Rayleigh Inverse Rayleigh Distribution: Structure and Properties

The Extension Odd Generalized Rayleigh Inverse Rayleigh (EOGRIR) distribution is a novel statistical model that leverages existing distribution families in a flexible manner. This model enhances the ability of standard distributions to analyze data. It makes it easier and faster to examine and model different types of lifetime and reliability data. The essay thoroughly examines the fundamental mathematical characteristics of the EOGRIR distribution. Some examples include series expansions, moments, the quantile, skewness, Rényi entropy, kurtosis, order statistics, and the moment generating function. These traits help us understand how the proposed distribution works and how its mathematical principles operate. We also examine methods for estimating parameters, with a focus on maximum likelihood estimates (MLE), to ensure that inference and parameter estimates are accurate. The EOGRIR distribution is likely to have a significant impact on statistics, as it offers a more flexible and comprehensive framework that may be superior to the existing ones