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A bound for bivariate probability of large deviations
Published online by Cambridge University Press: 14 July 2016
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 .
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- Copyright © Applied Probability Trust 1976
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