Extreme value modeling under power normalization

In this paper the mathematical modeling of extremes under power normalization is developed. An estimate of the shape parameter within the generalized extreme value distribution under power normalization is suggested. The statistical inference about the upper tail of a distribution function by using the power normalization is studied. Two models for generalized Pareto distribution under power normalization (GPDP) are given. Estimates for the shape and scale parameters within these GPDP’s are obtained. Finally, a simulation study illustrates and corroborates theoretical results.