Modeling risks from natural hazards with generalized additive models for location, scale and shape

Abstract

We investigate a new framework for estimating the frequency and severity of losses associated with catastrophic risks such as bushfires, storms and floods. We explore generalized additive models for location, scale and shape (GAMLSS) for the quantification of regional risk factors - geographical, weather and climate variables - with the aim of better quantifying the frequency and severity of catastrophic losses from natural perils. Due to the flexibility of the GAMLSS approach, we find a superior fit to empirical loss data for the applied models in comparison to generalized linear regression models typically applied in the literature. In particular the generalized beta distribution of the second kind (GB2) provides a good fit to the severity of losses. Including covariates in the calibration of the scale parameter, we obtain vastly differently shaped distributions for the predicted individual losses at different levels of the covariates. Testing the GAMLSS approach in an out-of-sample validation exercise, we also find support for a correct specification of the estimated models. More accurate models for the losses from natural hazards will help state and local government policy development, in particular for risk management and scenario planning for emergency services with respect to these perils.

Keywords: Generalized additive models for location scale and shape (GAMLSS); Natural hazards; Regional risk factors; Risk management.