Comparison Inequalities for One Sided Normal Probabilities |
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| Authors: | Liqing Yan |
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| Affiliation: | (1) Department of Environmental Engineering, Technical University of Crete, Chania, 73100, Greece;(2) Department Electrical and Computer Engineering, Polytechnic Institute of New York University, Brooklyn, NY 11201, USA |
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| Abstract: | Several sharp upper and lower bounds for the ratio of two normal probabilities $mathbb{P}Biggl(,bigcap_{i=1}^{n}bigl{xi^{(1)}_ileq mu_ibigr}Biggr)Big/mathbb{P}Biggl(,bigcap_{i=1}^{n}bigl{xi^{(0)}_ileq mu_ibigr}Biggr)$ 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. |
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