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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 (X1, Y1), (X2, Y2), …, (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 – nμx ≧ nt1;SY – nμY ≧ nt2} where Sx = Σ Xi, SY = Σ Yi,EYi = μY, EXi = μx and t1 > 0, t2 > 0. The bound is a function of the difference b — a, the correlation between Xi and Yi, μx and μY and t1 and t2.

Keywords

BIVARIATEUPPER BOUNDPROBABILITYEXPONENTIAL CONVERGENCE
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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