The generalised Pareto distribution (generalized Pareto distribution) arises in Extreme Value Theory (EVT). Its generalization is called Generalized Pareto Distribution. The Pareto distribution introduced above is one of the distributions with fat tails. from an unknown heavy-tailed distribution $$F$$ such that its tail distribution is regularly varying with the tail-index $$1/\xi$$ (hence, the corresponding shape parameter is $$\xi$$). 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. Assume that $$X_{1:n}=(X_{1},\cdots ,X_{n})$$ are $$n$$ observations (not need to be i.i.d.) the distribution of ‘threshold exceedances’, tends to a generalized Pareto distribution. In ad- dition, it is a "standardized distribution" in the sense that its mean and variance depend only on the parameter. https://en.wikipedia.org/wiki/Generalized_extreme_value_distribution If the relevant regularity conditions are satisfied then the tail of a distribution (above some suitably high threshold), i.e. Extreme value theory or extreme value analysis is a branch of statistics dealing with the extreme deviations from the median of probability distributions. Extreme value analysis is widely used in many disciplines, such as structural engineering, finance, earth sciences, traffic prediction, and geological engineering. This distribution plays an important role in the Extreme Value Theory. For example, EVA might be u To be specific, the tail distribution is described as