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Chebyshev Inequality with Estimated Mean and Variance
John G. Saw, Mark C. K. Yang and Tse Chin Mo
The American Statistician
Vol. 38, No. 2 (May, 1984), pp. 130-132
Stable URL: http://www.jstor.org/stable/2683249
Page Count: 3
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Chebyshev's inequality is investigated when the population mean and variance are estimated from a sample. The necessary modification to the inequality is simple and is actually valid when (a) the population moments do not exist and (b) the sample is exchangeably distributed. The latter case would include, for example, a sample taken without replacement from a finite population and the independent and identically distributed case.
The American Statistician © 1984 American Statistical Association