Improved Chebyshev inequality: new probability bounds with known supremum of PDF
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.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2018
- DOI:
- 10.48550/arXiv.1808.10770
- arXiv:
- arXiv:1808.10770
- Bibcode:
- 2018arXiv180810770N
- Keywords:
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- Statistics - Methodology;
- Mathematics - Probability;
- Mathematics - Statistics Theory
- E-Print:
- 7 pages, 2 figures