Comparison Inequalities for One Sided Normal Probabilities

Liqing Yan ()
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Liqing Yan: University of Florida

Journal of Theoretical Probability, 2009, vol. 22, issue 4, 827-836

Abstract: Abstract Several sharp upper and lower bounds for the ratio of two normal probabilities $$\mathbb{P}\Biggl(\,\bigcap_{i=1}^{n}\bigl\{\xi^{(1)}_i\leq \mu_i\bigr\}\Biggr)\Big/\mathbb{P}\Biggl(\,\bigcap_{i=1}^{n}\bigl\{\xi^{(0)}_i\leq \mu_i\bigr\}\Biggr)$$ are given in this paper for various cases, where (ξ 1 (0) ,ξ 2 (0) ,…,ξ n (0) ) and (ξ 1 (1) ,ξ 2 (1) , …,ξ n (1) ) are standard normal random variables with covariance matrices R 0=(r ij 0 ) and R 1=(r ij 1 ), respectively.

Keywords: Multivariate normal probability; Comparison inequality; 60G15; 60J65 (search for similar items in EconPapers)
Date: 2009
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DOI: 10.1007/s10959-009-0248-0

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