What can we infer from beyond the data? The statistics behind the analysis of risk events in the context of environmental studies

Abstract

When events occur outside the range of acceptable fluctuations, they may result in either (a) the events being more favourable than usual, or (b) the events being less favourable than usual. The latter has serious implications if their occurrences trigger a chain of subsequent negative events. Such events are termed `risk events'. Extreme Value Theory (EVT) is a tool that attempts to best estimate the probability of adversarial risk events. There are several environmental studies where extreme value methods have been used. In this paper, the behaviour of very high levels of the McArthur Fire Danger Index (FDI) at four sites in the Kruger National Park is described using the threshold exceedance approach in EVT. There is particular interest in whether there is dependence at high levels of the FDI series, seasonality and trend at each site. The authors will review how the model for threshold excesses, the Generalized Pareto distribution, has to be modified to incorporate these features and the effect this has on the parameter estimates