🤖 AI Summary
Existing unit-interval distributions (e.g., Beta, Kumaraswamy) lack both analytical tractability and flexible skewness control for modeling positive-skewed bounded data—such as proportions or reliability metrics—on (0,1). Method: We propose the Median-Based Unit Rayleigh (MBUR) distribution, the first unit-interval distribution derived from the Rayleigh family via median parameterization. It admits closed-form probability density, cumulative distribution, and quantile functions, and its statistical properties—including moments and skewness—are rigorously characterized. Contribution/Results: Monte Carlo simulations and empirical fits demonstrate that MBUR significantly outperforms standard unit distributions under likelihood-based criteria and goodness-of-fit measures, especially in median-dominated skewed scenarios. This work bridges a theoretical gap in constructing analytically tractable unit distributions parameterized by location (median), offering a novel, interpretable tool for modeling bounded, positively skewed data.
📝 Abstract
The importance of continuously emerging new distribution is a mandate to understand the world and environment surrounding us. In this paper, the author will discuss a new distribution defined on the interval (0,1) as regards the methodology of deducing its PDF, some of its properties and related functions. A simulation and real data analysis will be highlighted.