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

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  • Nishiyama, Tomohiro

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.

Suggested Citation

  • Nishiyama, Tomohiro, 2018. "Improved Chebyshev inequality: new probability bounds with known supremum of PDF," OSF Preprints h9zfn, Center for Open Science.
    • Handle: RePEc:osf:osfxxx:h9zfn
    DOI: 10.31219/osf.io/h9zfn
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    Cited by:

    1. Nishiyama, Tomohiro, 2019. "L^p-norm inequality using q-moment and its applications," OSF Preprints 7yzvj, Center for Open Science.

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