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A bound for bivariate probability of large deviations

Published online by Cambridge University Press:  14 July 2016

Matthew Goldstein
Matthew Goldstein*
Affiliation:
Baruch College, City University of New York
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Abstract

Suppose (X 1, Y 1), (X 2, Y 2), …, (Xn , Yn ) are independent random vectors such that a ≦ Xi ≦ b and a ≦ Yi ≦ b, i = 1, 2, …, n. An upper bound which exponentially converges to zero is derived for the probability Pr{Sx – nμ x ≧ nt 1;SY – nμY ≧ nt 2} where Sx = Σ Xi , SY = Σ Yi ,EYi = μY, EXi = μx and t 1 > 0, t2 > 0. The bound is a function of the difference b — a, the correlation between Xi and Yi, μx and μY and t 1 and t 2 .

Keywords

BIVARIATEUPPER BOUNDPROBABILITYEXPONENTIAL CONVERGENCE

Information

Type
Short Communications
Information
Journal of Applied Probability , Volume 13 , Issue 2 , June 1976, pp. 380 - 384
Copyright
Copyright © Applied Probability Trust 1976 

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References

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