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Bivariate Binomial Moments and Bonferroni-Type Inequalities

Author

Listed:
  • Qin Ding

    (FO7, University of Sydney)

  • Eugene Seneta

    (FO7, University of Sydney)

Abstract

We obtain bivariate forms of Gumbel’s, Fréchet’s and Chung’s linear inequalities for P(S ≥ u, T ≥ v) in terms of the bivariate binomial moments {S i, j }, 1 ≤ i ≤ k,1 ≤ j ≤ l of the joint distribution of (S, T). At u = v = 1, the Gumbel and Fréchet bounds improve monotonically with non-decreasing (k, l). The method of proof uses combinatorial identities, and reveals a multiplicative structure before taking expectation over sample points.

Suggested Citation

  • Qin Ding & Eugene Seneta, 2017. "Bivariate Binomial Moments and Bonferroni-Type Inequalities," Methodology and Computing in Applied Probability, Springer, vol. 19(1), pages 331-348, March.
    • Handle: RePEc:spr:metcap:v:19:y:2017:i:1:d:10.1007_s11009-016-9481-z
    DOI: 10.1007/s11009-016-9481-z
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    References listed on IDEAS

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    1. Galambos, J. & Xu, Y., 1995. "Bivariate Extension of the Method of Polynomials for Bonferroni-Type Inequalities," Journal of Multivariate Analysis, Elsevier, vol. 52(1), pages 131-139, January.
    2. Fred M. Hoppe & Eugene Seneta, 2012. "Gumbel’s Identity, Binomial Moments, and Bonferroni Sums," International Statistical Review, International Statistical Institute, vol. 80(2), pages 269-292, August.
    3. Chen, Tuhao & Seneta, E., 1995. "A note on bivariate Dawson-Sankoff-type bounds," Statistics & Probability Letters, Elsevier, vol. 24(2), pages 99-104, August.
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