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On probabilities in certain multivariate distributions: their dependence on correlations. (English) Zbl 0261.62041


MSC:

62H10 Multivariate distribution of statistics
60E05 Probability distributions: general theory
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References:

[1] T. W. Anderson: The integral of a symmetric unimodal function over a symmetric convex set and some probability inequalities. Proc. Amer. Math. Soc. 6 (1955), 170-176. · Zbl 0066.37402 · doi:10.2307/2032333
[2] F. A. Haight: Handbook of the Poisson distribution. J. Wiley & Sons, 1967. · Zbl 0152.37706
[3] P. Holgate: Estimation for the bivariate Poisson distribution. Biometrika 51 (1964), 241 - 245. · Zbl 0133.11802 · doi:10.1093/biomet/51.1-2.241
[4] 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 · doi:10.1214/aoms/1177698618
[5] C. G. Khatri: Further contributions to some inequalities for normal distributions and their applications to simultaneous confidence bounds. Ann. Inst. Statist. Math. 22 (1970), 451 - 458. · Zbl 0294.62013 · doi:10.1007/BF02506363
[6] A. W. Marshall I. Olkin: A multivariate exponential distribution. J. Amer. Statist. Assoc. 62 (1967), 30-44. · Zbl 0147.38106 · doi:10.2307/2282907
[7] Z. Šidák: Unequal numbers of observations in comparing several treatments with one control. (In Czech.) Apl. Mat. 7 (1962), 292-314.
[8] Z. Šidák: On probabilities of rectangles in multivariate Student distributions: their dependence on correlations. Ann. Math. Statist. 42 (1971), 169-175. · Zbl 0218.62063 · doi:10.1214/aoms/1177693504
[9] Z. Šidák: A note on C. G. Khatri’s and A. Scott’s papers on multivariate normal distributions. Submitted to Ann. Inst. Statist. Math. · Zbl 0368.62029 · doi:10.1007/BF02504636
[10] Z. Šidák: A chain of inequalities for some types of multivariate distributions, with nine special cases. Apl. Mat. 18 (1973), 110-118.
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