E. O. Kantonistova, I. V. Rodionov, “On tests to distinguish distribution tails invariant with respect to the scale parameter”, Dokl. RAN. Math. Inf. Proc. Upr., 2022, Volume 503,Pages <nobr>54

MATHEMATICS

On tests to distinguish distribution tails invariant with respect to the scale parameter

E. O. Kantonistova^a, I. V. Rodionov^b

^a National Research University Higher School of Economics, Moscow, Russia
^b Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

Abstract: We propose two tests to distinguish between separable classes of distribution tails, the first of which is invariant with respect to the scale parameter and the second is invariant with respect to both location and scale parameters. The asymptotic properties of the proposed tests are established. The distributions are not assumed to belong to any maximum domain of attraction.

Keywords: distribution tail, discrimination test, statistics of extremes, scale parameter, location parameter, Gumbel maximum domain of attraction.

UDC: 519.234.3

Presented: S. N. Vassilyev
Received: 03.12.2021
Revised: 13.01.2022
Accepted: 16.01.2022

DOI: 10.31857/S2686954322020114