Probability Inequalities for Multivariate Distributions with Dependence Structures
- 1 June 1984
- journal article
- research article
- Published by JSTOR in Journal of the American Statistical Association
- Vol. 79 (386) , 436
- https://doi.org/10.2307/2288287
Abstract
Let X 1, …, Xn be a sequence of random variables with a given positive or negative dependence structure. In this article we exploit the assumed dependence structure to construct a sequence of bounds for the P(Xi ε Ci ; i = 1, …, n), where Ci are infinite intervals of the same type. These bounds are superior to the well-known product bounds that are based solely on the marginal probabilities. Moreover, the new bounds can serve as respectable approximations for the P(Xi ε Ci ; i = 1, …, n).Keywords
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