Boundary Distributions with Respect to Chebyshev's Inequality
Peter Bias, Shawn Hedman & David Rose
Journal of Mathematics and Statistics, Volume 6, Issue 1, pp. 47–51 · doi.org/10.3844/jmssp.2010.47.51
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.
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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
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