Understand the derivation and characteristics of the Generalized Extreme Value and the Generalized Pareto distributions.
Free SOA Exam ASTAM (Advanced Short-Term Actuarial Mathematics) lesson in Severity Models. 10 min read, ~1,445 words.
GEV models the maximum of a block of losses; GPD models excesses above a high threshold. Both are indexed by a shape parameter: is heavy, is light, is bounded. Fisher-Tippett-Gnedenko: normalized block maxima converge to GEV (analogue of CLT for maxima). Pickands-Balkema-de Haan: excesses over a high threshold converge to...
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