On the Chvátal–Janson conjecture

Lucio Barabesi, Luca Pratelli and Pietro Rigo

Statistics & Probability Letters, 2023, vol. 194, issue C

Abstract: Let qm=P(X≤m), where m is a positive integer and X a binomial random variable with parameters n and m/n. Vašek Chvátal conjectured that, for fixed n≥2, qm attains its minimum when m is the integer closest to 2n/3. As shown by Svante Janson, this conjecture is true for large n. Here, we prove that the conjecture is actually true for every n≥2.

Keywords: Binomial distribution; Binomial tail probability; Bernoulli inequality (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167715222002577
Full text for ScienceDirect subscribers only

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:eee:stapro:v:194:y:2023:i:c:s0167715222002577

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.spl.2022.109744

Access Statistics for this article

Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul

More articles in Statistics & Probability Letters from Elsevier
Bibliographic data for series maintained by Catherine Liu ().