Modelling weather data by approximate regression quantiles.

Abstract

In the paper we introduce and explore an approximate regression quantiles method. It is based on a new interpretation of M-functionals as quantiles of probability distributions which are determined by the original distribution and the M-function. A correction factor can be applied and this brings the corrected M-functional, called an approximate quantile functional, very close to the quantiles of the original distribution. In the present paper we extend approximate quantile functionals onto parametric models and call them approximate regression quantiles . We next model probability distributions of some weather components as they vary over time. We use very simple, but non-linear, parametric models. By applying the approximate regression quantiles method we obtain five-curve summaries of the varying over time probability distributions of the considered weather components.