Teaser

What happens when the laws of chance meet the rare and the extreme—the floods of a century, the record heatwave, or the financial crash no one saw coming? This thesis ventures into that very territory, where mathematics tries to capture the seemingly unpredictable. Building on the foundations of extreme value theory, I explored how the classical tools begin to break down once real-world data refuses to fit the neat assumptions of textbooks. But what do I mean with neat assumptions? If you are a novice or only working tangential with statistics you may never stumbled upon the so called i.i.d. assumption:

• independent: The observations are (stochastically) independent from each other. This is of course highly unrealistic but statistical history has told, that this is not to bad as observations get more and more independent as there are larger and larger time-lags – meaning, there is a larger time distance between two observations.
• identically: The observations follow the same law. This is of course non-sense as it would basically discard climate-change – of course the weather in the year of 1900 follows a different distribution than the weather in the year of 2025. The just explained gap between the real world and existing (extreme value) statistical literature was tackled in this masters thesis.

I developed new theoretical results, adapted statistical methods to more complex settings, and tested their performance in large-scale simulations. The outcome: a fresh perspective on how to model extremes when the rules of stability no longer apply.

Link to the thesis (written in german).