Geodesic
Variance upper bounds and a probability inequality for discrete α-unimodality
Applicationes Mathematicae, Tome 27 (2000) no. 4, pp. 403-410.

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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.
DOI : 10.4064/am-27-4-403-410
Keywords: probability inequality, variance, upper and lower bounds, discrete unimodality

M. Ageel 1

1 
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M. Ageel. Variance upper bounds and a probability inequality for discrete α-unimodality. Applicationes Mathematicae, Tome 27 (2000) no. 4, pp. 403-410. doi : 10.4064/am-27-4-403-410. http://geodesic.mathdoc.fr/articles/10.4064/am-27-4-403-410/

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