Boundary distributions with respect to Chebyshev's inequality
Boundary distributions with respect to Chebyshev's inequality
Date
2010
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Authors
Bias, Peter V.
Hedman, Shawn
Rose, David
Journal Title
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Publisher
Science Publications
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.
Description
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Article
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Keywords
Statistics, Variables (Mathematics), Chebyshev’s inequality
Citation
Bias, P. V., 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