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.
Acknowledgments
The authors appreciate the anonymous reviewers for their careful reading of the manuscript and comments.