JDS Journal of Data Science 1683-86021680-743X1680-743X School of Statistics, Renmin University of China JDS1120 10.6339/24-JDS1120 Statistical Data Science Discrete Extremes HitzAdrien S.adrien.hitz@ahx.ai1 DavisRichard A.rdavis@stat.columbia.edu2 SamorodnitskyGennadygs18@cornell.edu3 Department of Statistics, University of Oxford, 24-29 St Giles, Oxford OX1 3LB, UK Department of Statistics, Columbia University, 1255 Amsterdam Avenue, New York, NY, US School of Operations Research and Information Engineering, Cornell University, 220 Rhodes Hall, Ithaca, NY, US 20242322024224524536 Supplementary Material

The 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.

28120243112024 2024 The Author(s). Published by the School of Statistics and the Center for Applied Statistics, Renmin University of China.2024 Open access article under the CC BY license.

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.

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