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A Note on Bernstein's Bivariate Inequality

Published online by Cambridge University Press:  20 November 2018

K. Mullen
K. Mullen*
Affiliation:
Department of Mathematics, University of Guelph, Guelph, Ont. NIG 2W1
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Summary

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An upper bound for P[Σ Xi≥tσ, Σ Yi ≥ tσ], where (Xi, Yi ), i = 1, 2, …, n are bounded independent random variables, was given by Mullen (1973). An improvement to the bound is possible without further assumptions.

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 22 , Issue 3 , 01 September 1979, pp. 371 - 375
Copyright
Copyright © Canadian Mathematical Society 1979

References

1. Bennett, G., (1962), Probability Inequalities for the Sum of Independent Random Variables. J. Amer. Statist. Ass. 57, 33-45.Google Scholar
2. Bernstein, S., (1924), Sur une modification de l' inégalité de Tchebichef (In Russian, French Summary). Ann. Sci. Inst. Sew. Ukraine Sect. Math I. Google Scholar
3. Mullen, K., (1973), Bernstein's Inequality in the Bivariate Case. Can. Math. Bull 16, 83-86.Google Scholar