A Novel Unit Distribution Named As Median Based Unit Rayleigh (MBUR): Properties and Estimations

Background and aim In this paper, the author introduces the Median-Based Unit Rayleigh (MBUR) distribution, a newly formulated statistical distribution defined exclusively on the interval (0, 1). The development of such distributions is essential for enhancing our comprehension of phenomena modeled through ratios and proportions. Methods The paper provides a detailed derivation of the probability density function (PDF) for the MBUR distribution, thoroughly articulating each phase of the derivation process. The analysis extends to a rigorous examination of the MBUR distribution's properties, encompassing related functions crucial for statistical evaluation, including the cumulative distribution function (CDF), survival function, hazard rate function, and quantile function. These functions are integral to elucidating the distribution's behavior and characteristics.In addition to theoretical insights, the author examines various methodologies for parameter estimation relevant to the MBUR distribution. A detailed overview of the statistical techniques used for parameter estimation is provided, highlighting their respective strengths and weaknesses. Results To underpin these methodologies, extensive simulation studies will be conducted, demonstrating the efficacy and robustness of the proposed estimation techniques. These simulations will facilitate a comparative analysis to evaluate the fit of the MBUR distribution across diverse datasets. Discussion Additionally, the paper incorporates real data analyses to showcase the empirical utility of the MBUR distribution. This will involve a systematic comparison of the MBUR distribution's performance against wellestablished unit distributions, such as the beta and Kumaraswamy distributions, highlighting its advantages and adaptability in modeling practical scenarios. This thorough exploration aims to provide significant contributions to the expanding domain of statistical distributions. Conclusion: MBUR is an advanced statistical model designed to effectively manage a wide variety of skewed data distributions. It has been shown to outperform traditional distributions, such as the beta and Kumaraswamy distributions, in the analysis of certain real-world datasets. One of the main advantages of MBUR is its capability to estimate parameters using just a single parameter, which offers both flexibility and efficiency in modeling complex data patterns. This characteristic not only simplifies the estimation process but also enhances its applicability across different fields where skewed data is prevalent.