The New Generalized Odd Median Based Unit Rayleigh with a New Shape Oscillating Hazard Rate Function

In this paper, the author presents the generalized form of the Median-Based Unit Rayleigh (MBUR) distribution, a novel statistical distribution that is specifically defined within the interval (0, 1) expressing oscillating hazard rate function. This generalization adds a new parameter to the MBUR distribution that significantly addresses the unique characteristics of data represented as ratios and proportions, which are commonly encountered in various fields of research. The establishment of this generalization aims to deepen our understanding of these phenomena by providing a robust framework for analysis. The paper offers a thorough and meticulous derivation of the probability density function (PDF) for the MBUR distribution, illuminating each phase of the process with clarity and precision. It delves deep into the intricacies of the MBUR distribution's properties, presenting a rigorous examination of the accompanying functions that are vital for robust statistical evaluation. These functions—comprising the cumulative distribution function (CDF), survival function, hazard rate and reversed hazard rate function. The paper discusses real data analysis and how the generalization improves such analysis.