A Generalized Class of Skew Distributions and Parametric Quantile Regression Models

This paper proposes a generalized class of univariate skew distributions that are constructed through mixture of two scaled normal distributions. The proposed skew distributions with the skewness parameter defined in the (0,1) interval allow us to have an application on parametric quantile regression. Expressing a skew distribution as a scale mixture of normal can facilitate the estimation procedure via the Bayesian Markov Chain Monte Carlo methods. We conduct two simulation studies on skew error regression models and parametric quantile regression models with two corresponding empirical studies on the U.S. market return and infant birthweight data where we obtain satisfactory results