Extreme event analysis: estimating boundaries for data extremity / Zuraida Jaafar

In practical applications of statistical modelling, the phenomena under investigation often involve many data points representing rare events with extremely high or low values compared to the typical range. These extreme events can significantly impact the data distribution, exhibiting long and heavy tails. The occurrence of extreme events can be observed across various disciplines, including climatology, earth sciences, ecology, engineering, hydrology, and social sciences. However, a critical question arises in extreme events analysis: How far can we reliably determine the extremity of data? One of the most fundamental problems in the field of extreme value models is selecting a threshold value, a boundary or cutoff point used to determine the extremity of the data (McPhillips et al., 2018). The choice of the thresholds needs to be done properly, as a high threshold value will reduce the bias but increase the variance for the estimators while choosing a low value will give the opposite effect (Scarrott & MacDonald, 2012). Choosing the appropriate threshold value can help ensure that these extreme values are accurately identified and included in the analysis, leading to more accurate predictions and better decision-making.