Multivariate product-type lower bounds (Q2748436)
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scientific article; zbMATH DE number 1659439
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Multivariate product-type lower bounds |
scientific article; zbMATH DE number 1659439 |
Statements
Multivariate product-type lower bounds (English)
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23 June 2002
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multivariate inequality
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spanning tree
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positive dependence
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product-type bound
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linear programming
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bivariate Fréchet optimal bound
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\(\text{MTP}_2\)
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This article is devoted to obtain product-type bounds in a multivariate probability inequality setting. The paper describes two results for product-type inequalities for \(k\) sets of weak and strong sub-Markovian events, and proves a theorem on multivariate product-type inequalities for \(\text{MTP}_2\) random variables. Using graph theory and bivariate Fréchet optimal lower bounds derived by linear programming techniques, the authors construct product-type lower bounds for the probability of the intersection among unions of \(k\) sets of events. A numerical example illustrates the use of the proposed method, and compares the new bound with already existing bounds.
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