Estimation of Frechet disribution parameters by joint distribution of ' m ' extremes

Abstract

By using three medians a quick method of estimation of the parameters of the Fréchet distribution was given by Gumbel (1965). Tiago de Oliveira (1972) estimated the parameters of the distribution using the maximum likelihood method. Recently Singh (1987) proposed the maximum likelihood estimates based on m extremes of several samples. However, the joint information of the lower extremes should be used because the information is necessary to be recorded to achieve the first extremes. In this paper the maximum likelihood estimates using the joint asymptotic distribution function of m extremes of several samples are derived. The variances and covariances of the estimates for every additional lower order extreme (up to the 20-th lower extreme) and for different values of the shape parameter are computed in order to examine the increase in the efficiency of the estimates due to the additional information of the lower order extremes.