| Title:
|
Remarks on Anděl's paper “On multiple normal probabilities of rectangles” (English) |
| Author:
|
Šidák, Zbyněk |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
16 |
| Issue:
|
3 |
| Year:
|
1971 |
| Pages:
|
182-187 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper contains come brief remarks on the preceding paper by J. Anděl. First, it discusses some simplifications in the bound for the remainder of Anděl's series. Second, it deals with a special case of covariance matrices for which this series has only non-negative terms. () |
| MSC:
|
62H99 |
| idZBL:
|
Zbl 0223.62081 |
| idMR:
|
MR0285062 |
| DOI:
|
10.21136/AM.1971.103344 |
| . |
| Date available:
|
2008-05-20T17:50:32Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103344 |
| . |
| Reference:
|
[1] J. Anděl: On multiple normal probabilities of rectangles.Aplikace matematiky 16 (1971), 172-181. MR 0285061 |
| Reference:
|
12] R. N. Curnow C. W. Dunnett: The numerical evaluation of certain multivariate normal integrals.Ann. Math. Statist. 33 (1962), 571-579. MR 0137234, 10.1214/aoms/1177706443 |
| Reference:
|
[3] O. J. Dunn: Estimation of the means of dependent variables.Ann. Math. Statist. 29 (1958), 1095-1111. Zbl 0092.36702, MR 0101589, 10.1080/01621459.1955.10501294 |
| Reference:
|
[4] 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 |
| Reference:
|
[5] M. Fiedler V. Pták: On matrices with non-positive off-diagonal elements and positive principal minors.Czech. Math. J. 12 (87) (1962), 382-400. MR 0142565 |
| Reference:
|
[6] F. R. Gantmacher: Matrizenrechnung.2. Auflage, Deutscher Verlag der Wissenschaften, Berlin 1965. MR 0206013, 10.1214/aoms/1177698618 |
| 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 |
| Reference:
|
[8] M. Parodi: La localisation des valeurs caractéristiques des matrices et ses applications.Gauthier-Villars, Paris 1959. MR 0110719, 10.1214/aoms/1177693504 |
| Reference:
|
[9] Z. Šidák: On probabilities of rectangles in multivariate Student distributions: their dependence on correlations.Ann. Math. Statist. 42 (1971), in print. MR 0278354 |
| . |
