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Chebyshev Inequality with Estimated Mean and Variance

1984; Taylor & Francis; Volume: 38; Issue: 2 Linguagem: Inglês

10.1080/00031305.1984.10483182

1537-2731

John G. Saw, Mark C. K. Yang, Tse Chin Mo,

Statistical Distribution Estimation and Applications

Abstract 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.