EconPapers    
Economics at your fingertips  
 

On upper and lower bounds for probabilities of combinations of events

Andrei N. Frolov

Statistics & Probability Letters, 2021, vol. 173, issue C

Abstract: We derive new upper and lower bounds for probabilities that r or at least r out of n events occur. These bounds are optimal since they can turn to equalities. We describe a method of constructing of such bounds. It can be applied in case of measurable spaces and measures with sign as well. We also obtain bounds for conditional probabilities of combinations of events given σ-field. Averaging of both sides of inequalities for conditional probabilities can yield better bounds for unconditional probabilities.

Keywords: Bonferroni inequalities; Chung–Erdős inequality; Bounds for probabilities of unions of events; Bounds for probabilities of combinations of events; Measure of unions; Borel–Cantelli lemma (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: Track citations by RSS feed

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167715221000353
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:173:y:2021:i:c:s0167715221000353

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.2021.109073

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 ().

 
Page updated 2021-06-30
Handle: RePEc:eee:stapro:v:173:y:2021:i:c:s0167715221000353