We improve the known upper and lower bounds for the probability of the fact that exactly kievents should occur in a group consisting of nievents simultaneously for all i= 1, 2, ..., d.
Unable to display preview. Download preview PDF.
- 1.J. Galambos and Y. Xu, “Two sets of multivariate Bonferroni-type inequalities,” in: H. N. Nagaraja et al. (eds), Statistical Theory and ApplicationsSpringer, Heidelberg (1996), pp. 29–36.Google Scholar
- 2.M. Sobel and V. R. R. Uppuluri, “On Bonferroni-type inequalities of the same degree for the probability of unions and intersections,” Ann. Math. Statist., 43, 1549–1558 (1972).Google Scholar
- 3.F. M. Hoppe, “Beyond inclusion-and exclusion: Natural identities for P[exactly tevents] and P[at least tevents] and resulting inequalities,” Int. Statist. Rev., 61, 435–446 (1993).Google Scholar
- 4.T. Chen and E. Seneta, “Multivariate Bonferroni-type lower bounds,” J. Appl. Probab., 33, 729–740 (1996).Google Scholar
- 5.J. Galambos and M.-Y. Lee, “Further studies of bivariate Bonferroni-type inequalities,” J. Appl. Probab., 31A, 63–69 (1994).Google Scholar
- 6.J. Galambos, The Asymptotic Theory of Extreme Order Statistics, Wiley, New York (1978).Google Scholar
- 7.E. Recsei and E. Seneta, “Bonferroni-type inequalities,” Adv. Appl. Probab., 19, 508–511 (1987).Google Scholar
- 8.J. Galambos and I. Simonelli, Bonferroni-Type Inequalities with Applications, Spinger, New York (1996).Google Scholar
- 9.R. M. Meyer, “Note on a “multivariate” form of Bonferroni's inequalities,” Ann. Math. Statist., 40, 692–693 (1996).Google Scholar
- 10.E. Seneta, “Degree, iteration and permutation in improving Bonferroni-type bounds,” Austral. J. Statist., 30A, 27–38 (1988).Google Scholar
© Plenum Publishing Corporation 2000