Geodesic
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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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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/

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