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On probabilities in certain multivariate distributions: their dependence on correlations
Applications of Mathematics, Tome 18 (1973) no. 2, pp. 128-135
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First, under a multivariate normal distribution with all correlations of the form $Q_{ij}=b_ib_j$ (where $-1\leq b_i, b_j\leq 1$), the probabilities of certain convex symmetric regions are shown to be, roughly speaking, non-decreasing functions of $\left|Q_{ij}\right|$. Second, under an equicorrelated normal distribution, the probabilieties of certain regions (which need be neither convex nor symmetric) are shown to be non-decreasing functions of the correlations. Third, some inequalities for special cases of multivariate exponential and Poisson distributions are given.
First, under a multivariate normal distribution with all correlations of the form $Q_{ij}=b_ib_j$ (where $-1\leq b_i, b_j\leq 1$), the probabilities of certain convex symmetric regions are shown to be, roughly speaking, non-decreasing functions of $\left|Q_{ij}\right|$. Second, under an equicorrelated normal distribution, the probabilieties of certain regions (which need be neither convex nor symmetric) are shown to be non-decreasing functions of the correlations. Third, some inequalities for special cases of multivariate exponential and Poisson distributions are given.
DOI : 10.21136/AM.1973.103459
Classification : 60E05, 62H05, 62H10 
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Šidák, Zbyněk. On probabilities in certain multivariate distributions: their dependence on correlations. Applications of Mathematics, Tome 18 (1973) no. 2, pp. 128-135. doi: 10.21136/AM.1973.103459

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