Discrete Extremes

2017/07/17 by Adrien S. Hitz, Hitz, Adrien, Richard A. Davis +3 · 3 citations
Computer Science · Economics, Econometrics and Finance · Mathematics · #Bayesian Methods and Mixture Models #FOS: Mathematics #Financial Risk and Volatility Modeling #Statistical Distribution Estimation and Applications #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1707.05033

openalex publication_date 2017/07/17 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28

Abstract

Our contribution is to widen the scope of extreme value analysis applied to discrete-valued data. Extreme values of a random variable X are commonly modeled using the generalized Pareto distribution, a method that often gives good results in practice. When X 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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