Improved Chebyshev inequality: new probability bounds with known supremum of PDF

08/31/2018

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by   Tomohiro Nishiyama, et al.

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In this paper, we derive new probability bounds for Chebyshev's inequality if the supremum of the probability density function is known. This result holds for one-dimensional or multivariate continuous probability distributions with finite mean and variance (covariance matrix). We also show that the similar result holds for specific discrete probability distributions.