Improved Chebyshev inequality: new probability bounds with known supremum of PDF
arXiv:1808.10770
Abstract
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.
arXiv comment7 pages, 2 figures