Modelling Extreme Rainfalls Using Generalized Additive Models for Location, Scale and Shape Parameters

Abstract

This study aims to model the nonlinear relationship between the daily amount of extreme rainfall and significant predictor variables by the Generalized additive models for location, scale and shape parameters (GAMLSS). Statistical modelling of extreme rainfall is an essential means of assessing hydrological impacts of changing rainfall patterns resulting from climate variability. Extreme value theory states that only three types of distributions are needed to model the extreme events (Gumbel, Frechet and Weibull) for large samples. However we identify the model that best characterizes the behaviour of the extreme rainfall data is the lognormal model with respect to Akaike Information Criteria (AIC). In the simulation study, we propose to approximate the location parameter for the Gumbel (maximum) and Lognormal distributions using cubic splines. Results reveal that the approximated mean function by the GAMLSS modelling converges to the true mean function. Moreover, the bias is decreasing rapidly for the true fixed parameter. Although GAMLSS procedure utilizes extreme rainfall data, the same methodology can be applied to other variables in many areas.