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

Table 3

Inverse of the quantile links and names in VGAMextra. “Approximate” means that Newton–Raphson or bisection is used to approximate the inverse. All family functions except for normal1sdff(), which is in VGAMextra, are in VGAM.

Distribution		Inverse	Family function	Link in VGAMextra
Exponential			exponential()	expQlink()
Benini			benini1()	benini1Qlink()
Rayleigh			rayleigh()	rayleighQlink()
Gamma		Approximate	gamma1()	gamma1Qlink()
Maxwell			maxwell()	maxwellQlink()
Topp–Leone^†			topple()	toppleQlink()
N()			normal1sdff()	normal1sdQlink()

denotes the inverse of the logit() transformation.