On the bounds for the expected maxima of~random~samples with known expected maxima of two samples of smaller size
Teoriâ veroâtnostej i ee primeneniâ, Tome 68 (2023) no. 1, pp. 4-20
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Our aim in the present paper is to give a new representation of the previously known estimates and further investigate upper and lower bounds for expected maxima of $n$ independent and identically distributed (i.i.d.) standardized random variables (r.v.'s)
from known expected maxima of $m$ and $p$ r.v.'s with the same distribution, where $1$.
A new representation is obtained from expansion of the inverse distribution function in a system of orthonormal functions on the unit interval.
A criterion for attainability of the resulting bounds is put forward. We also obtain asymptotic properties of normed bounds for maxima expectations and normed maxima of r.v.'s with distribution where a criterion for attainability of these bound holds.
Keywords:
expected maxima, orthogonal expansion.
@article{TVP_2023_68_1_a0,
author = {D. V. Ivanov},
title = {On the bounds for the expected maxima of~random~samples with known expected maxima of two samples of smaller size},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {4--20},
publisher = {mathdoc},
volume = {68},
number = {1},
year = {2023},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_2023_68_1_a0/}
}
TY - JOUR AU - D. V. Ivanov TI - On the bounds for the expected maxima of~random~samples with known expected maxima of two samples of smaller size JO - Teoriâ veroâtnostej i ee primeneniâ PY - 2023 SP - 4 EP - 20 VL - 68 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TVP_2023_68_1_a0/ LA - ru ID - TVP_2023_68_1_a0 ER -
%0 Journal Article %A D. V. Ivanov %T On the bounds for the expected maxima of~random~samples with known expected maxima of two samples of smaller size %J Teoriâ veroâtnostej i ee primeneniâ %D 2023 %P 4-20 %V 68 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/TVP_2023_68_1_a0/ %G ru %F TVP_2023_68_1_a0
D. V. Ivanov. On the bounds for the expected maxima of~random~samples with known expected maxima of two samples of smaller size. Teoriâ veroâtnostej i ee primeneniâ, Tome 68 (2023) no. 1, pp. 4-20. http://geodesic.mathdoc.fr/item/TVP_2023_68_1_a0/