Modeling and Fitting Quantile Distributions and Regressions

SYNOPTIC ABSTRACT

This paper surveys the development of distributions defined by their quantile functions in both distributional and regression situations. It considers issues of both model construction and fitting. In particular it advocates the use of the ordered data in distributional estimation and seeks to emphasise that regression based on the use of quantiles is far broader in application than that usually encompassed by the phrase ‘quantile regression’. This survey covers parametric rather than non-parametric approaches.

Key Words and Phrases:

• distributions
• lambda distributions
• quantile functions
• model construction
• estimation
• parametric quantile regression