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ISSN: 1549-3644 (Print)
ISSN: 1558-6359 (Online)
Research Article Open Access

Boundary Distributions with Respect to Chebyshev's Inequality

Peter Bias, Shawn Hedman and David Rose

Abstract

Variables whose distributions achieve the boundary value of Chebyshev’s inequality are characterized and it is found that non-constant variables with this property are symmetric discrete with at most three values. Nevertheless, the bound of Chebyshev’s inequality remains optimal for the class of continuous variables.

Journal of Mathematics and Statistics
Volume 6 No. 1, 2010, 47-51

DOI: https://doi.org/10.3844/jmssp.2010.47.51

Submitted On: 15 January 2010 Published On: 31 March 2010

How to Cite: Bias, P., Hedman, S. & Rose, D. (2010). Boundary Distributions with Respect to Chebyshev's Inequality. Journal of Mathematics and Statistics, 6(1), 47-51. https://doi.org/10.3844/jmssp.2010.47.51

Open AccessCopyright: © 2010 Peter Bias, Shawn Hedman and David Rose. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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Keywords

  • Chebyshev’s inequality
  • k-boundary variable
  • k-condensed variable
  • nearly k-boundary variable