О критериях проверки гипотезы об эквивалентности хвостов распределений

Доклады Российской академии наук. Математика, информатика, процессы управления (ранее - Доклады Академии Наук. Математика). 2022. Т. 507. № 1. С. 36–39.

Kantonistova E., Родионов И. В.

We propose a method for testing the hypothesis about the equivalence of the distribution tail of
observed data and a certain distribution tail, which is the analogue of the goodness-of-fit hypothesis for statistics
of extremes. The method is based on a new data transformation moving k largest order statistics of a
sample from the standard uniform distribution U[0,1] to random variables asymptotically similar to a sample
of size k from ГU[0,1]. We prove that tests built by applying the proposed method are consistent on the widest
alternative, specifically, on the negation of the null hypothesis.

Keywords: критерий согласия, эквивалентность, equivalence, хвост распределения, статистика экстремумов, distribution tail, goodness-of-fit tests, statistics of extremes