Testing for Trends in Excesses Over a Threshold Using the Generalized Pareto Distribution

Abstract

The Generalized Pareto Distribution (GPD) is used for modeling exceedances over thresholds. The general form of the GPD depends on three parameters: the location parameter µ; the scale parameter (β > 0); and the shape parameter (−∞ < ξ < ∞). This work restricts attention to the case where µ = 0 and shows that, as ξ decreases while β is kept fixed, the family of GPD(ξ, β) distributions increases in the usual stochastic order. This property is used for testing the significance of trends in the size of the exceedances over high thresholds in a time series consisting of ozone measurements.