Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
권호 표지

AN IMPROVED LOWER BOUNDS OF UNIVARIATE BONFERRONI-TYPE INEQUALITY

  • Received : 2009.02.24
  • Accepted : 2009.06.05
  • Published : 2009.06.30
Download PDF
⟨ Previous Next ⟩

Abstract

Let $A_1,\;A_2,\;{\cdots},\;A_n$ be a sequence of events on a given probability space. Let $m_n$ be the number of those $A_{i}{^{\prime}}s$ which occur. We establish an improved lower bounds of Univariate Bonferroni-Type inequality by using the linearity of binomial moments $S_1,\;S_2,\;S_3,\;S_4$ and$S_5$.

Keywords

References

  1. J. Galambos and Y. Xu, A new method for generating Bonferroni-type inequalities by iteration, Math. Proc. Camb. Soc. 107 (1998), 601-607.
  2. J. Galambos, Bomferroni-type Inequalities with Application, Sprinfer-Verlag New York Berlin Heidelberg, 1996.
  3. B. J. Margolin and W. Maurer, Test of the Kolmogorov-Smirnor type for exponential data with unknown scale and related problems, Biometrika 63 (1976), 149-160. https://doi.org/10.1093/biomet/63.1.149
  4. Seneta. E. Degree, Iteration and permutation in improving Bonferroni-type bounds, Austrial. J. Statist. 30A (1988), 27-38. https://doi.org/10.1111/j.1467-842X.1988.tb00462.x