arXiv subjects

Merle Mendel

Publications and source records attributed to Merle Mendel.

2 recordsLinked to original sources

arXiv2025

Parameter Estimation and Seasonal Modification of the Fractional Poisson Process with Application to Vorticity Extremes over the North Atlantic

The fractional Poisson process (FPP) generalizes the standard Poisson process by replacing exponentially distributed return times with Mittag-Leffler distributed ones with an extra tail parameter, allowing for greater flexibility. The FPP has been applied in various fields, such as modeling occurrences of extratropical cyclones in meteorology and solar flares in physics. We propose a new estimation method for the parameters of the FPP, based on minimizing the distance between the empirical and the theoretical distribution at selected quantiles. We conduct an extensive simulation study to evaluate the advantages and limitations of the new estimation method and to compare it with several competing estimators, some of which have not yet been examined in the Mittag-Leffler setting. To enhance the applicability of the FPP in real-world scenarios, particularly in meteorology, we propose a method for incorporating seasonality into the FPP through distance-based weighting. We then analyze the return times of relative vorticity extremes in the North Atlantic-European region using our seasonal modeling approach.

stat.AP↗

arXiv2023

Models for temporal clustering of extreme events with applications to mid-latitude winter cyclones

The occurrence of extreme events like heavy precipitation or storms at a certain location often shows a clustering behaviour and is thus not described well by a Poisson process. We construct a general model for the inter-exceedance times in between extreme events which combines different candidate models for such behaviour. One of them is formulated in terms of clusters of dependent events with exponential inter-exceedance times in between clusters, while the other assumes independent events separated by heavy-tailed inter-exceedance times. We propose a modification of the Cram\'er-von Mises distance for fitting the combined model. The resulting estimator turns out to be competitive with specialised estimators if the data stem from one of the two submodels. Our modelling approach thus allows us to distinguish these different data generating mechanisms without the need of a-priori model selection. An application to mid-latitude winter cyclones illustrates the usefulness of our work as the combination of the two mechanisms improves the descriptions of such occurrences at many places.

stat.ME↗