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Chebyshev Inequalities for Unimodal Distributions
Thomas M. Sellke and Sarah H. Sellke
The American Statistician
Vol. 51, No. 1 (Feb., 1997), pp. 34-40
Stable URL: http://www.jstor.org/stable/2684690
Page Count: 7
You can always find the topics here!Topics: Random variables, Chebyshevs inequality, Tangent lines, Convexity, Statistics, Probability distributions, Minimum value, Line segments, Tangents, Mathematical theorems
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Let g be an even function on R that is nondecreasing on [0, ∞), and let k be a positive constant. For random variables X that are unimodal with mode 0, and for random variables X that are unimodal with an unspecified mode, we derive sharp upper bounds on P(|X| ≥ k) in terms of Eg(X). The proofs consist largely of drawing a chord and a few tangent lines on graphs of cdf's.
The American Statistician © 1997 American Statistical Association