Discrimination between close hypotheses about Weibull and log-Weibull type distributions by the higher order statistics

The proposed paper discusses the problem of discrimination between close hypotheses about distributions belonging to the Gumbel maximum domain of attraction. The distinctive feature of the proposed work is using only k higher order statistics of the sample in the construction of criteria, because there are many situations when we do not know the whole sample, as it occurs in the problems linked with safety, life span, catastrofes, sea level and other. This work is the first in the series of the author's works that deal with the statistics of extrema.