Modeling Bounded Response Variables Using Quantile Regression Based on Arc Tangent Unit Weibull Distribution

Abstract

This study introduces the Arc Tangent Unit Weibull (ATUW) distribution, a model for proportion based educational attainment data bounded within the unit interval. the ATUW model, which is derived by applying an arc tangent transformation to the classical Weibull distribution, provides greater flexibility in capturing skewed outcomes and extreme values. To estimate the parameters of the proposed model, several estimation methods are applied and their performance are compared through simulation studies, focusing on bias and mean squared error under varying conditions. The model is further reparametrized as the Quantile Arc Tangent Unit Weibull (QATUW) distribution, enabling its use in quantile regression analysis. Application to district-level data from the Bangladesh Multiple Indicator Cluster Survey (2019) reveals maternal education and age at first school enrollment as significant predictors of children’s higher educational attainment. Comparative results demonstrate that the QATUW model outperforms traditional Beta and Kumaraswamy distributions, particularly in modeling extreme quantiles, offering stronger evidence for educational policy and planning.

Dhaka Univ. J. Sci. 74(2): 361–366, 2026 (July)