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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:
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


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