ABSTRACT
This chapter focuses on issues arising in the statistical analysis of losses from extreme weather and climate events, especially for the purpose of the detection of trends. Making use of extreme value theory, we attempt to reconcile the different approaches to modeling the probability distribution of losses, fitting the lognormal distribution to all the loss data versus fitting the generalized Pareto distribution to only extreme high losses. Both approaches are capable of producing an apparent heavy tail characteristic of loss data. Still we recommend use of the generalized Pareto distribution when the focus is on catastrophic disasters. Variability and uncertainty in loss estimates are important because they can introduce bias into adjusted losses. We show how the standard technique for converting insured loss to total loss can result in a substantial underestimation on average. Further, the normalization of losses to remove shifts in societal vulnerabilities over time, such as increases in population, can introduce an artificial decreasing trend. Such an effect could well hide any real trend in losses due to climate change. Applications involve losses from U.S. billion-dollar weather and climate disasters, as well as losses caused by hurricanes alone.
