A new parametric quantile regression model based on an Owen distribution

Quantile regression is a versatile statistical tool for modeling conditional quantiles, offering a comprehensive view of the relationship between explanatory and response variables. This technique is widely used in fields like economics, finance, environmental science, and psychology. This paper introduces a new quantile regression model based on the Owen distribution, which provides flexibility in capturing quantile-specific relationships. The model parameters are estimated using maximum likelihood estimation, with a detailed discussion on the estimation process. Diagnostic measures, including a pseudo-R2 statistic, quantile residuals, and generalized Cook's distance, are proposed to assess model adequacy and identify influential data points. Monte Carlo simulations are employed to evaluate the estimators' performance. The model's effectiveness is illustrated through an application to Chilean household income data, highlighting its advantages over conventional quantile regression models. Implemented in the R programming language, this model is accessible for practical use, offering a valuable addition to the quantile regression field and suggesting promising directions for further research and application across disciplines.