New Link Functions for Distribution–Specific Quantile Regression Based on Vector Generalized Linear and Additive Models

Table 2

New link functions for the quantiles of some 1–parameter distributions. The selected function is also shown.

Distribution		Support of	Quantile function	Function	Quantile link
Exponential				log–link
Benini				log–link
Rayleigh				log–link
Gamma			No closed–form	log–link
Maxwell^†				log–link
Topp–Leone				logit	logit
1–par Normal^‡				identity

qgamma() is the quantile function of the standard gamma distribution in R.
logit.
^‡, with erf() denoting the error function.