A0358
Title: Modeling waiting times of clustered extreme events with application to mid-latitude winter cyclones
Authors: Katharina Hees - University of Siegen (Germany)
Roland Fried - TU Dortmund University (Germany)
Christina Mathieu - TU Dortmund University (Germany) [presenting]
Abstract: For many applications in the field of extreme value theory, both the frequency of the occurrence and the return times of extreme events are of great interest, such as in climate research in the study of extreme mid-latitude cyclones. Traditionally, a Poisson process is assumed as a model for the occurrence of extreme events so that the waiting times between two successive exceedances are i.i.d. exponentially distributed. However, this does not properly reflect the temporal clustering that often occurs in data. A prior study provided a modelling framework for such clustering behaviour under the assumption that the observations are realizations of a strictly stationary process with an existing extremal index. In such cases, the scaled waiting times between extreme events are approximately distributed as a mixture of an exponential distribution and a Dirac measure of zero. A recent study proposed another model for clustered extreme events based on a fractional Poisson process, leading to Mittag-Leffler distributed inter-exceedance times. The purpose is to introduce a generalized model that includes exponential, mixed, and Mittag-Leffler distributed waiting times as special cases. The suitability of a minimum distance method is verified based on a modification of the Cramr-von Mises distance for joint estimation of the model parameters and an application on climate data is shown.
