Bivariate Binomial Moments and Bonferroni-Type Inequalities

Qin Ding () and Eugene Seneta ()
Additional contact information
Qin Ding: FO7, University of Sydney
Eugene Seneta: FO7, University of Sydney

Methodology and Computing in Applied Probability, 2017, vol. 19, issue 1, 331-348

Abstract: 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.

Keywords: Bivariate binomial moments; Gumbel’s inequality; Combinatorial identity; Bonferroni-type inequalities; Primary 60E05; Secondary 60C05 (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s11009-016-9481-z Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:metcap:v:19:y:2017:i:1:d:10.1007_s11009-016-9481-z

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/11009

DOI: 10.1007/s11009-016-9481-z

Access Statistics for this article

Methodology and Computing in Applied Probability is currently edited by Joseph Glaz

More articles in Methodology and Computing in Applied Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().