Lower and Upper Bounds for Rectangular Probabilities |
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| Authors: | Amir Ahmadi-Javid |
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| Affiliation: | 1. Department of Industrial Engineering , Amirkabir University of Technology (Tehran Polytechnic) , Tehran, Iran ahmadi_javid@aut.ac.ir |
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| Abstract: | This article presents some results showing how rectangular probabilities can be studied using copula theory. These results lead us to develop new lower and upper bounds for rectangular probabilities which can be computed efficiently. The new bounds are compared with the ones obtained from the generalized Fréchet–Hoeffding bounds and Bonferroni-type inequalities. |
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| Keywords: | Bonferroni-type inequalities Copula theory Fréchet–Hoeffding bounds Invariant copulas under truncation Multivariate distribution Probability of a rectangle |
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