A novel quantile regression for fractiles based on unit logistic exponential distribution

Continuous developments in unit interval distributions have shown effectiveness in modeling proportional data. However, challenges persist in diverse dispersion characteristics in real-world scenarios. This study introduces the unit logistic-exponential (ULE) distribution, a flexible probability model built upon the logistic-exponential distribution and designed for data confined to the unit interval. The statistical properties of the ULE distribution were studied, and parameter estimation through maximum likelihood estimation, Bayesian methods, maximum product spacings, and least squares estimates were conducted. A thorough simulation analysis using numerical techniques such as the quasi-Newton method and Markov chain Monte Carlo highlights the performance of the estimation methods, emphasizing their accuracy and reliability. The study reveals that the ULE distribution, paired with tools like randomized quantile and Cox-Snell residuals, provides robust assessments of goodness of fit, making it well-suited for real-world applications. Key findings demonstrate that the unit logistic-exponential distribution captures diverse data patterns effectively and improves reliability assessment in practical contexts. When applied to two real-world datasets—one from the medical field and the other from the economic sector—the ULE distribution consistently outperforms existing unit interval models, showcasing lower error rates and enhanced flexibility in tail behavior. These results underline the distribution's potential impact in areas requiring precise proportions modeling, ultimately supporting better decision-making and predictive analyses.