BOUNDS ON PROBABILITY FOR THE OCCURRENCE OF EXACTLY r, t OUT OF m, n EVENTS

  • Published : 1997.04.01

Abstract

Let $A_1,A_2,\cdots,A_m$ and $B_1,B_2,\cdots,B_n$ be two sequences of events on a given probability space. Let $X_m$ and $Y_n$, respectively, be the number of those $A_i$ and $B_j$, which occur we establish new upper and lower bounds on the probability $P(X=r, Y=t)$ which improve upper bounds and classical lower bounds in terms of the bivariate binomial moment $S_{r,t},S_{r+1,t},S_{r,t+1}$ and $S_{r+1,t+1}$.

Keywords

References

  1. J. Amer. Stat. v.70 order statistics of samples from multivariate distributions J. Galambos
  2. Journal of Applied probability v.31A Further studies of Bonferroni-Type inequalities J. Galambos;M.-Y. Lee
  3. Journal of Multivariate Analysis v.52 Bivariate Extension of the Method of Polynomials for Bonferroni-Type Inequalities J. Galambos;Y. Xu
  4. Ann. Math. Statist v.40 Note on a multivariate form of Bonferroni's inequalities R. M. Meyer