On Compound Distributions for Natural Disaster Modelling in Kenya

Abstract

Kenyan communities are exposed to natural disasters by an amalgamation of factors such as poverty, aridity, and settlements in areas susceptible to natural disasters or in areas with poor infrastructure. This is expected to increase due to the effects of climate change. In an attempt to explain some of these variabilities, we model the extreme damages from natural disasters in Kenya by developing a compound distribution that takes into account both the frequency and the severity of the extreme events. The resulting distribution is based on a threshold model and compound extreme value distribution. For frequency of events exceeding a threshold of 150,000, we found that it follows a negative binomial distribution, while severity of exceedance follows a generalized Pareto distribution. This distribution fits the data well and is found to be a better model for natural disasters in Kenya than the traditional extreme value threshold model.