Boundary distributions with respect to Chebyshev's inequality
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.
Research Subject Categories::MATHEMATICS
Bias, P., Hedman, S., Rose, D. (2010). Boundary distributions with respect to Chebyshev's inequality. Journal of Mathematics and Statistics 6(1)L 47-51.