On the Estimation of the Distribution Tail Index

Abstract

This thesis is devoted to the study of a regression estimator for estimating the tail index of the heavy-tailed distribution. In particular, it is shown that the considered estimator is in general based on the method of weighted least squares. The main objective of the thesis is extend the work of Zyl and schall; 2012, for estimating the shape parameter of the Frechet distribution. By deriving the large sample variances and using the inverse of the approximate variance to calculate the weights for this estimator. Simulation study using R statistical software is carried out to evaluate performance of a new estimator wich has been shown to perform better than other considered methods estimator based on order statistics for small and large sample size, and in case of real data.