Economic Impact of Extreme Climate Events: An Approach Based on Penultimate Extreme Value Theory

• Activity Number: 545
• Type: Invited
• Date/Time: Wednesday, August 1, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Rick Katz*+
• Companies: National Center for Atmospheric Research
• Keywords: Damage function ; Generalized extreme value distribution ; Generalized Pareto distribution ; Hazard rate ; Power transformation

Abstract

Much attention has been devoted to the statistics of extreme climate events (e.g., floods, heat waves, hurricanes, or tornadoes). However, at least in part because of a dearth of data, not much is known about the precise form of the distribution of economic damage caused by such events. Here the statistical theory of extreme values is applied to suggest an explanation for how the apparent upper tail behavior of the distribution of economic damage might well be consistent with that for the underlying natural phenomenon.

Rather than standard asymptotic (or "ultimate") theory, it turns out that a "penultimate" approximation is required. As an example, we focus on the economic damage from hurricanes and its relationship to storm intensity (i.e., as measured by maximum wind velocity). If this relationship 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, notwithstanding storm intensity having a bounded upper tail.