Title: Exponentiated Generalized Pareto Distribution: Properties and applications towards Extreme Value Theory,
Abstract: The Generalized Pareto Distribution (GPD) plays a central role in modelling
heavy tail phenomena in many applications. Applying the GPD to actual datasets
however is a non-trivial task. One common way suggested in the literature to
investigate the tail behaviour is to take logarithm to the original dataset in
order to reduce the sample variability. Inspired by this, we propose and study
the Exponentiated Generalized Pareto Distribution (exGPD), which is created via
log-transform of the GPD variable. After introducing the exGPD we derive
various distributional quantities, including the moment generating function,
tail risk measures. As an application we also develop a plot as an alternative
to the Hill plot to identify the tail index of heavy tailed datasets, based on
the moment matching for the exGPD. Various numerical analyses with both
simulated and actual datasets show that the proposed plot works well.