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The proposed paper discusses the problem of discrimination between closehypotheses about distributions belonging to the Gumbel maximum domain ofattraction. The distinctive feature of the proposed work is using only k higherorder statistics of the sample in the construction of criteria, because thereare many situations when we do not know the whole sample, as it occurs in theproblems linked with safety, life span, catastrofes, sea level and other. Thiswork is the first in the series of the author's works that deal with thestatistics of extrema.

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