Inequalities for probability contents of convex sets via geometric average
It is shown that: If (X1, X2) is a permutation invariant central convex unimodal random vector and if A is a symmetric (about 0) permutation invariant convex set then P{(aX1, X2/a) [set membership, variant] A} is nondecreasing as a varies from )+ to 1 and is non-increasing as a varies from 1 to [infinity] (that is, P{(a1X1, a2X2) [epsilon] A} is a Schur-concave function of (log a1, log a2). Some extensions of this result for the n-dimensional case are discussed. Applications are given for elliptically contoured distributions and scale parameter families.
Year of publication: |
1988
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Authors: | Shaked, Moshe ; Tong, Y. L. |
Published in: |
Journal of Multivariate Analysis. - Elsevier, ISSN 0047-259X. - Vol. 24.1988, 2, p. 330-340
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Publisher: |
Elsevier |
Keywords: | probability inequalities majorization probability content of rectangles and ellipsoids Schur-concavity log-concavity functions decresing in transposition multivariate unimodality elliptically contoured distributions peakedness |
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