Flexible parametric quantile regression model

This article introduces regression quantile models using both RS and FKML generalised lambda distributions (GLD) and demonstrates the versatility of proposed models for a range of linear/non linear and heteroscedastic/homoscedastic empirical data. Owing to the rich shapes of GLDs, GLD quantile regression is a competitive flexible model compared to standard quantile regression. The proposed method has some major advantages: 1) it provides a reference line which is very robust to outliers with the attractive property of zero mean residuals and 2) it gives a unified, elegant quantile regression model from the reference line with smooth regression coefficients across different quantiles. The proposed method has wide applications given the flexibility of GLDs. The goodness of fit of the proposed model can be assessed via QQ plots and Kolmogorov-Smirnov test, to ensure the appropriateness of statistical inference under consideration.