IMPROVED INFERENCE FOR THE GENERALIZED PARETO DISTRIBUTION UNDER LINEAR, POWER AND EXPONENTIAL NORMALIZATION.

We discuss three estimation methods: the method of moments, probability weighted moments, and L-moments for the scale parameter and the extreme value index in the generalized Pareto distribution under linear normalization. Moreover, we adapt these methods to use for the generalized Pareto distribution under power and exponential normalizations. A simulation study is conducted to compare the three methods on the three models and determine which is the best, which turned out to be the probability weighted moments. A new computational technique for improving fitting quality is proposed and tested on two real-world data sets using the probability weighted moments. We looked back at various maximal data sets that had previously been addressed in the literature and for which the generalized extreme value distribution under linear normalization had failed to adequately explain them. We use the suggested procedure to find good fits. [ABSTRACT FROM AUTHOR]