Title:
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A chain of inequalities for some types of multivariate distributions, with nine special cases (English) |
Author:
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Šidák, Zbyněk |
Language:
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English |
Journal:
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Aplikace matematiky |
ISSN:
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0373-6725 |
Volume:
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18 |
Issue:
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2 |
Year:
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1973 |
Pages:
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110-118 |
Summary lang:
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English |
Summary lang:
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Czech |
. |
Category:
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math |
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Summary:
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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:
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60E05 |
MSC:
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62E10 |
MSC:
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62H10 |
idZBL:
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Zbl 0261.62042 |
idMR:
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MR0315842 |
DOI:
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10.21136/AM.1973.103457 |
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Date available:
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2008-05-20T17:55:37Z |
Last updated:
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2020-07-28 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/103457 |
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Reference:
|
[1] O. J. Dunn: Estimation of the medians for dependent variables.Ann. Math. Statist. 30 (1959), 192-197. Zbl 0090.36404, MR 0103563, 10.1214/aoms/1177706374 |
Reference:
|
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Reference:
|
[3] F. A. Haight: Handbook of the Poisson distribution.J. Wiley & Sons, 1967. Zbl 0152.37706, MR 0208713 |
Reference:
|
[4] P. Holgate: Estimation for the bivariate Poisson distribution.Biometrika 51 (1964), 241-245. Zbl 0133.11802, MR 0172374, 10.1093/biomet/51.1-2.241 |
Reference:
|
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Reference:
|
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Reference:
|
[7] C. G. Khatri: On certain inequalities for normal distributions and their applications to simultaneous confidence bounds.Ann. Math. Statist. 38 (1967), 1853-1867. Zbl 0155.27103, MR 0220392, 10.1214/aoms/1177698618 |
Reference:
|
[8] A. W. Marshall I. Olkin: A multivariate exponential distribution.J. Amer. Statist. Assoc. 62 (1967), 30-44. MR 0215400, 10.1080/01621459.1967.10482885 |
Reference:
|
[9] R. G. Miller, Jr.: Simultaneous statistical inference.McGraw-Hill Book Company, 1966. Zbl 0192.25702, MR 0215441 |
Reference:
|
[10] Z. Šidák: Rectangular confidence regions for the means of multivariate normal distributions.J. Amer. Statist. Assoc. 62 (1967), 626-633. MR 0216666 |
Reference:
|
[11] Z. Šidák: On probabilities of rectangles in multivariate Student distributions: their dependence on correlations.Ann. Math. Statist. 42 (1971), 169-175. MR 0278354, 10.1214/aoms/1177693504 |
Reference:
|
[12] D. Slepian: The one-sided barrier problem for Gaussian noise.Bell System Tech. J. 41 (1962), 463-501. MR 0133183, 10.1002/j.1538-7305.1962.tb02419.x |
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:
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[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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