Abstract

Much attention has been devoted to the statistics of extreme geophysical phenomena. However, at least in part because of a dearth of data, not much is known about the corresponding distribution of economic damage caused by extreme events. In this chapter, the statistical theory of extreme values ... Show moreMuch attention has been devoted to the statistics of extreme geophysical phenomena. However, at least in part because of a dearth of data, not much is known about the corresponding distribution of economic damage caused by extreme events. In this chapter, the statistical theory of extreme values is applied to provide an explanation for how the apparent upper tail behavior of the distribution of economic damage is not necessarily inconsistent with that for the underlying geophysical phenomenon. Rather than standard asymptotic (or "ultimate") theory, it turns out that a "penultimate" (or second-order) approximation is required. If this relationship (or damage function) is in the form of a power transformation as suggested by physical considerations, then penultimate extreme value theory would imply, at least under a wide range of plausible conditions, that the distribution of economic damage would have an apparent heavy tail, even if storm intensity has an apparent bounded upper tail. The economic damage from hurricanes and its relationship to storm intensity, as measured by maximum wind speed at landfall, is the focus of an example. Show less