Discussion: A comparison of GAMLSS with quantile regression

A discussion on the relative merits of quantile, expectile and GAMLSS regression models is given. We contrast the ‘complete distribution models’ provided by GAMLSS to the ‘distribution free models’ provided by quantile (and expectile) regression. We argue that in general, a flexibility parametric distribution assumption has several advantages allowing possible focusing on specific aspects of the data, model comparison and model diagnostics. A new method for concentrating only on the tail of the distributions is suggested combining quantile regression and GAMLSS.