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A note on C. G. Khatri’s and A. Scott’s papers on multivariate normal distributions. (English) Zbl 0368.62029


MSC:

62H05 Characterization and structure theory for multivariate probability distributions; copulas
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References:

[1] Halperin, M. (1967). An inequality on a bivariate Student’s ”t” distribution.J. Amer. Statist. Assoc.,62, 603–606. · Zbl 0158.18502 · doi:10.2307/2283987
[2] Jogdeo, K. (1970). A simple proof of an inequality for multivariate normal probabilities of rectangles.Ann. Math. Statist.,41, 1357–1359. · Zbl 0225.62068 · doi:10.1214/aoms/1177696913
[3] Khatri, C. G. (1967). On certain inequalities for normal distributions and their applications to simultaneous confidence bounds.Ann. Math. Statist.,38, 1853–1867. · Zbl 0155.27103 · doi:10.1214/aoms/1177698618
[4] Khatri, C. G. (1970). Further contributions to some inequalities for normal distributions and their applications to simultaneous confidence bounds.Ann. Inst. Statist. Math.,22, 451–458. · Zbl 0294.62013 · doi:10.1007/BF02506363
[5] Scott, A. (1967). A note on conservative confidence regions for the mean of a multivariate normal.Ann. Math. Statist.,38, 278–280. Correction:Ann. Math. Statist.,39 (1968), 2161. · Zbl 0155.26201 · doi:10.1214/aoms/1177699083
[6] Šidák, Z. (1967). Rectangular confidence regions for the means of multivariate normal distributions,J. Amer. Statist. Assoc.,62, 626–633. · Zbl 0158.17705 · doi:10.2307/2283989
[7] Šidák, Z. (1967). Rectangular confidence regions for the means of multivariate normal distributions, II,Statist. Lab. Publ., No. 7, Michigan State Univ. · Zbl 0158.17705
[8] Šidák, Z. (1968). On multivariate normal probabilities of rectangles: their dependence on correlations.Ann. Math. Statist.,39, 1425–1434. · Zbl 0169.50102
[9] Šidák, Z. (1971). On probabilities of rectangles in multivariate Student distributions: their dependence on correlations,Ann. Math. Statist.,42, 169–175. · Zbl 0218.62063 · doi:10.1214/aoms/1177693504
[10] Tong, Y. L. (1970). Some probability inequalities of multivariate normal and multivariatet, J. Amer. Statist. Assoc.,65, 1243–1247. · Zbl 0225.62067 · doi:10.2307/2284290
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