Variance upper bounds for discrete α-unimodal distributions defined on a finite support are established. These bounds depend on the support and the unimodality index α. They increase as the unimodality index α increases. More information about the underlying distributions yields tighter upper bounds for the variance. A parameter-free Bernstein-type upper bound is derived for the probability that the sum S of n independent and identically distributed discrete α-unimodal random variables exceeds its mean E(S) by a positive value nt. The bound for P{S-nμ ≥ nt} depends on the range of the summands, the sample size n, the unimodality index α and the positive number t.
@article{bwmeta1.element.bwnjournal-article-zmv27i4p403bwm,
author = {M. Ageel},
title = {Variance upper bounds and a probability inequality for discrete $\alpha$-unimodality},
journal = {Applicationes Mathematicae},
volume = {27},
year = {2000},
pages = {403-410},
zbl = {1045.60012},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-zmv27i4p403bwm}
}
Ageel, M. Variance upper bounds and a probability inequality for discrete α-unimodality. Applicationes Mathematicae, Tome 27 (2000) pp. 403-410. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-zmv27i4p403bwm/
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