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Title: A chain of inequalities for some types of multivariate distributions, with nine special cases (English)
Author: Šidák, Zbyněk
Language: English
Journal: Aplikace matematiky
ISSN: 0373-6725
Volume: 18
Issue: 2
Year: 1973
Pages: 110-118
Summary lang: English
Summary lang: Czech
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Category: math
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Summary: Generalizing the result by Y. L. Tong, a chain of inequalities for probabilities in some types of multivariate distributions is proved. These inequalities embrace a large number of interesting special cases. Nine illustrations are given: cases of multivariate equicorrelated normal, $t,\chi^2$, Poisson, exponential distributions, normal and rank statistics for comparing many treatments with one control, order statistics used in estimating quantiles, and characteristic roots of covariance matrices in certain multiple sampling. ()
MSC: 60E05
MSC: 62E10
MSC: 62H10
idZBL: Zbl 0261.62042
idMR: MR0315842
DOI: 10.21136/AM.1973.103457
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Date available: 2008-05-20T17:55:37Z
Last updated: 2020-07-28
Stable URL: http://hdl.handle.net/10338.dmlcz/103457
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Reference: [13] R. G. D. Steel: A multiple comparison rank sum test: treatments versus control.Biometrics 15 (1959), 560-572. Zbl 0097.13404, MR 0108869, 10.2307/2527654
Reference: [14] R. G. D. Steel: A multiple comparison sign test: treatments versus control.J. Amer. Statist. Assoc. 54 (1959), 767-775. Zbl 0090.36003, MR 0109396
Reference: [15] Y. L. Tong: Some probability inequalities of multivariate normal and multivariate t.J. Amer. Statist. Assoc. 65 (1970), 1243-1247. Zbl 0225.62067, 10.1080/01621459.1970.10481159
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