Bounded Data Modeling with the Extended Bradford Distribution: Modal Regression Approach and Applications

Modeling bounded response variables is an important problem in computational statistics, especially in applications involving skewed, heavy-tailed data. In such cases, the modal regression is a robust alternative to traditional mean-based modeling approaches. In this study, a new bounded distribution, called the extended Bradford distribution, is proposed as a flexible extension of the classical Bradford distribution. By incorporating an additional shape parameter, the corresponding model can capture various shape structures, such as left and right skewness, increasing, and bathtub hazard shapes. The new distribution provides an explicit expression for the mode, making it suitable for modal regression. Based on this, a parametric modal regression model is developed, and parameter estimation is performed via the maximum likelihood method. The behavior of the estimators is investigated through comprehensive simulation studies. The practical usefulness of the proposed model is illustrated through applications, where the proposed model provides an improved fit compared to several competing models. In addition, an interactive R Shiny application is developed to facilitate the implementation, computation, and visualization of the model.