On Bounds for Probabilities of Combinations of Events, the Jordan Formula, and the Bonferroni Inequalities

Standard

On Bounds for Probabilities of Combinations of Events, the Jordan Formula, and the Bonferroni Inequalities. / Frolov, A. N. .

в: Vestnik St. Petersburg University: Mathematics, Том 52, № 2, 2019, стр. 178-186.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

BibTeX

@article{3994d5d1dafc4fc19d3c154cc754cda7,

title = "On Bounds for Probabilities of Combinations of Events, the Jordan Formula, and the Bonferroni Inequalities",

abstract = "This paper presents a method for deriving optimal lower and upper bounds for probabilities and conditional probabilities (given a σ-field) for various combinations of events. The optimality is understood as the possibility that inequalities become equalities for some sets of events. New generalizations of the Jordan formula and the Bonferroni inequalities are obtained. The corresponding conditional versions of these results are also considered.",

keywords = "Bonferroni inequalities, Jordan formula, probabilities of combinations of events, probabilities of occurrence of several events",

author = "Frolov, {A. N.}",

note = "Frolov, A.N. Vestnik St.Petersb. Univ.Math. (2019) 52: 178. https://doi.org/10.1134/S1063454119020055",

year = "2019",

doi = "10.1134/S1063454119020055",

language = "English",

volume = "52",

pages = "178--186",

journal = "Vestnik St. Petersburg University: Mathematics",

issn = "1063-4541",

publisher = "Pleiades Publishing",

number = "2",

}

RIS

TY - JOUR

T1 - On Bounds for Probabilities of Combinations of Events, the Jordan Formula, and the Bonferroni Inequalities

AU - Frolov, A. N.

N1 - Frolov, A.N. Vestnik St.Petersb. Univ.Math. (2019) 52: 178. https://doi.org/10.1134/S1063454119020055

PY - 2019

Y1 - 2019

N2 - This paper presents a method for deriving optimal lower and upper bounds for probabilities and conditional probabilities (given a σ-field) for various combinations of events. The optimality is understood as the possibility that inequalities become equalities for some sets of events. New generalizations of the Jordan formula and the Bonferroni inequalities are obtained. The corresponding conditional versions of these results are also considered.

AB - This paper presents a method for deriving optimal lower and upper bounds for probabilities and conditional probabilities (given a σ-field) for various combinations of events. The optimality is understood as the possibility that inequalities become equalities for some sets of events. New generalizations of the Jordan formula and the Bonferroni inequalities are obtained. The corresponding conditional versions of these results are also considered.

KW - Bonferroni inequalities

KW - Jordan formula

KW - probabilities of combinations of events

KW - probabilities of occurrence of several events

UR - http://www.scopus.com/inward/record.url?scp=85067207499&partnerID=8YFLogxK

U2 - 10.1134/S1063454119020055

DO - 10.1134/S1063454119020055

M3 - Article

VL - 52

SP - 178

EP - 186

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 2

ER -

ID: 42786843