TY - JOUR

T1 - On upper and lower bounds for probabilities of combinations of events

AU - Frolov, Andrei N.

N1 - Publisher Copyright: © 2021 Elsevier B.V. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2021/6

Y1 - 2021/6

N2 - 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.

AB - 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.

KW - Bonferroni inequalities

KW - Borel–Cantelli lemma

KW - Bounds for probabilities of combinations of events

KW - Bounds for probabilities of unions of events

KW - Chung–Erdős inequality

KW - Measure of unions

KW - Chung-Erdos inequality

KW - INEQUALITIES

KW - Borel-Cantelli lemma

KW - LEAST R

KW - STRINGENT BOUNDS

KW - INTERSECTION

KW - UNIONS

UR - http://www.scopus.com/inward/record.url?scp=85102390788&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/36b93c80-fe4d-3627-b8a4-4a48b5b98b34/

U2 - 10.1016/j.spl.2021.109073

DO - 10.1016/j.spl.2021.109073

M3 - Article

AN - SCOPUS:85102390788

VL - 173

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

SN - 0167-7152

M1 - 109073

ER -