A Novel Quantile Regression Approach Based on the Zubair-Unit Rayleigh Model

Abstract

In this paper, we introduce a novel two-parameter distribution on the unit interval, termed the Zubair-Unit Rayleigh distribution. We derive its fundamental statistical properties and evaluate various parameter estimation techniques through a comprehensive simulation study. Building upon this foundation, we develop a new quantile regression model based on the proposed distribution. Applications to real-world datasets demonstrate that both the new distribution and its corresponding regression model provide a superior fit and greater flexibility compared to existing alternatives.