A Class Of Generalization Location Invariant Heavy Tailed Index Estimator

Due to the concern of the extreme events,heavy-tailed distribution which character-izes the peak thick tail has been seen lots of fields like finance,insurance,computer sci-ence,hydrology,meteorology and so on.The parameter γ is called tail index which plays a main role in heavy tailed distribution,for it contains varies of information about the tail.As a result,the index γ is studied by many researchers.In this paper,firstly,we introduced the heavy-tailed distribution and its theoretical ba-sis,and detailed various of methods for heavy-tailed index.Next,based on the statistic Mn (α)(k0,k) and the generalization estimator γn(α)(k),we put forward a new class of heavy tail index es-timator which is location invariant, and discuss its consistency and asymptotic normality under the second order condition in the extreme value theory,and the new estimator is simu-lated from the point of MSE on the choice of α. Finally, the estimators γnH(k0,k),γnH(k0, k) and γn(α) (k0, k) are compared under Frechet, Burr and Pareto models from the point of mean value and MSE respectively, and the new estimator has the better performance.