Variance upper bounds and a probability inequality for discrete α-unimodality

Volume 27 / 2000

M. Ageel Applicationes Mathematicae 27 (2000), 403-410 DOI: 10.4064/am-27-4-403-410


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.


  • M. Ageel

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