Comparison on estimations for the extremal index

Vergelijken van schatters van de extreme index

Bachelor thesis (2020)

Authors

J.A.M.L. Clercx Electrical Engineering, Mathematics and Computer Science

Contributors

J. Cai Statistics - EEMCS (mentor)
L.E. Meester Applied Probability - EEMCS (graduation committee member)
Faculty
Electrical Engineering, Mathematics and Computer Science, Electrical Engineering, Mathematics and Computer Science
Copyright: © 2020 Josephine Clercx
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Published Date

01-06-2020

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Abstract

The clustering of events can have a large impact on society. The extremal index $\theta$ tells how much extreme events cluster. We will compare different types of estimators in this project. First, we review the extremes of different sequences which have different values of $\theta$. We have found significant differences between the extremes. Then, 2 different types of estimators are introduced which both use different ways to divide the data, using disjoint blocks and using sliding blocks. The optimal block lengths are simulated for all those estimators. Using those block lengths, $\theta$ is simulated with all the estimators. From the simulations we conclude that the estimators using sliding blocks perform better. The best-performed estimator that we found from the simulations is used to estimate $\theta$ on data from the KNMI, comparing wind gusts and precipitation at weather stations De Bilt and Vlissingen.