Heavy tail index estimator through weighted least-squares rank regression

In this paper, we proposed a weighted least square estimator based method to estimate the shape parameter of the Frechet distribution. We show the performance of the proposed estimator in a simulation study, it is found that the considered weighted estimation method shows better performance than the maximum likelihood estimation. Maximum product of spacing estimation and least-squares in terms of bias and root mean square error for most of the considered sample sizes. In addition, a real example from Danish data is provided to demonstrate the performance of the considered method.