Discrete Extremes
Volume 22, Issue 4 (2024), pp. 524–536
Pub. online: 23 February 2024
Type: Statistical Data Science
Open Access
Open Access
Received
28 January 2024
28 January 2024
Accepted
31 January 2024
31 January 2024
Published
23 February 2024
23 February 2024
Abstract
Our contribution is to widen the scope of extreme value analysis applied to discrete-valued data. Extreme values of a random variable are commonly modeled using the generalized Pareto distribution, a peak-over-threshold method that often gives good results in practice. When data is discrete, we propose two other methods using a discrete generalized Pareto and a generalized Zipf distribution respectively. Both are theoretically motivated and we show that they perform well in estimating rare events in several simulated and real data cases such as word frequency, tornado outbreaks and multiple births.
Supplementary material
Supplementary MaterialThe data and code supporting this article are available in the GitHub repository at https://github.com/adhi1000/discrete_extremes. This archive includes the file Simulated Data.R , which details the simulation study discussed in Section 3, and the files Word Frequency.R , Tornado.R and Multiple Birth.R , which replicate the real data analysis presented in Section 4.
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