Chebyshev Inequalities for Unimodal Distributions

American Statistician

Volumn 51, Issue 1, 1997, Pages 34-40

  Sellke, Thomas M ^a   Sellke, Sarah H ^a  

^a PURDUE UNIVERSITY   (United States)

Author keywords

Convexity; Gauss inequality; Vysochanski Petunin inequality

Indexed keywords

EID: 0042230142     PISSN: 00031305     EISSN: 15372731     Source Type: Journal    
DOI: 10.1080/00031305.1997.10473584     Document Type: Article

References (9)

1. Cramer, H. (1946), Mathematical Methods of Statistics, Princeton, NJ: Princeton University Press.
2. Dharmadhikari, S., and Joag-dev, K. (1985), “The Gauss-Tchebyshev Inequality for Unimodal Distributions,” Theory of Probability and Its Applications, 30, 867-871.
3. Dharmadhikari, S., and Joag-dev, K. (1988), Unimodality, Convexity, and Applications, New York: Academic Press.
4. Gauss, C. F. (1823), “Theoria Combinationis Observationum Erroribus Minimis Obnoxiae, Pars Prior,” Commentationes Societatis Regiae Sci-entiarum Gottingensis Recentiores, 5.
5. Pukelsheim, F. (1994), “The Three Sigma Rule,” The American Statistician, 48, 88-91.
6. Sellke, T. (1996), “Generalized Gauss-Chebyshev Inequalities for Unimodal Distributions,” Metrika, 43, 107-121.
7. Vysochanskit, D. F., and Petunin, Y. I. (1980), “Justification of the 3er Rule for Unimodal Distributions,” Theory of Probability and Mathematical Statistics, 21, 25-36.
8. Vysochanskit, D. F., and Petunin, Y. I. (1983), “A Remark on the Paper ‘Justification of the 3
9. Winckler, A. (1866), “Allgemeine Satze zur Theorie der unregelmassigen Beobachtungsfehler,” Sitzungsberichte der Mathamatisch—natur-wissenschaftlichen Classe der Kaiserlichen Akademie der Wis-senschaften zu Wien, Zweite Abteilung, 53, 6-11.