Journal of Data Science

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.

In this work, we introduce a new distribution for modeling the extreme values. Some important mathematical properties of the new model are derived. We assess the performance of the maximum likelihood method in terms of biases and mean squared errors by means of a simulation study. The new model is better than some other important competitive models in modeling the repair times data and the breaking stress data.