Adaptive threshold selection for extreme value analysis to predict return levels of ozone layer depletion

Extreme value theory is a method for modeling and measuring risks associated with rare events and it has gained prominence in risk management in recent years. Further, it is a probabilistic framework that deals with extremes and seeks to build new methodologies and also to model the characteristics of extreme events, and predict the occurrence of such extreme events. Typically, we focus on the peak-over-threshold method, which involves inspecting generalized Pareto distribution for exceedances above a particularly high threshold. The practical implementation of identifying exceedances over the threshold in practice requires two areas of research to be addressed which are establishing a suitable threshold and then fitting an appropriate distribution to estimate the parameters. The selection of an appropriate threshold is critical in threshold-based techniques for extreme value analysis. In this paper, we proposed an adaptive threshold selection technique, that employs the Gastwirth estimator as a trimming point to remove non-extremes, and we developed a new three-parameter GPerks distribution, which is then compared to the conventional methods. We applied the classical and proposed methods to identify the extreme values in real-life applications, here we discussed the dataset of the ozone hole area in Antarctica. The return level of ozone concentration after 2, 5, 10, and 20 years is estimated based on the proposed method.