| 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 |
| . |
| Category:
|
math |
| . |
| 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 |
| . |
| Date available:
|
2008-05-20T17:55:37Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103457 |
| . |
| 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:
|
[2] C. W. Dunnett: A multiple comparison procedure for comparing several treatments with a control.J. Amer. Statist. Assoc. 50 (1955), 1096-1121. Zbl 0066.12603, 10.1080/01621459.1955.10501294 |
| 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:
|
[5] D. R. Jensen: An inequality for a class of bivariate chi-square distributions.J. Amer. Statist. Assoc. 64 (1969), 333-336. Zbl 0175.17306, MR 0240896, 10.1080/01621459.1969.10500978 |
| Reference:
|
[6] D. R. Jensen M. Q. Jones: Simultaneous confidence intervals for variances.J. Amer. Statist. Assoc. 64 (1969), 324-332. 10.1080/01621459.1969.10500977 |
| 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:
|
[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 |
| . |
