Tail index and right endpoint estimators Extreme value theory or extreme value analysis is a branch of statistics dealing with the extreme deviations from the median of probability distributions. It seeks to assess, from a given ordered sample of a given random variable, the probability of events that are more extreme than any previously observed.
Extreme value analysis is widely used in many disciplines, such as structural engineering, finance, earth sciences, traffic prediction, and geological engineering.
For the tail index, a parameter that decides of which of the three extreme value distributions is underlying the data, several estimators are presented. The fundamental role of the tail index is added to the statistical tests of choice of domains of attraction.
This analysis allows estimating high quantiles and the right endpoint of the support of the variable under study, when it is finite. This code is applied to data of the female triple jump (outdoor) (30/06/2022).