Improvement of the Ushakov bound

Kensho Kobayashi and Hidekazu Tanaka

Communications in Statistics - Theory and Methods, 2021, vol. 50, issue 24, 5929-5940

Abstract: Considering a discrete unimodal distribution, an upper bound on a tail probability about a mode is suggested, which can be shown to be sharper than both the Bienaymé-Chebyshev bound and the Ushakov bound. Furthermore, by using the suggested bound, an upper bound on the probability outside the range of three standard deviations is given when a mean equals a mode.

Date: 2021
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DOI: 10.1080/03610926.2020.1737878

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