title: On inequalities for probabilities of joint occurrence of several events
metadata.name: dc.contributor.author
metadata.value: Frolov, Andrei N.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2018-09-18T11:49:23Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2018-09-18T11:49:23Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2018-09
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Frolov A.N. On inequalities for probabilities of joint occurrence of several events. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2018, vol. 5 (63), issue 3, pp. 464–476.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu01.2018.310
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/14889
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: Various inequalities for probabilities of joint occurrence of several events are widely used in
  combinatorial analysis, probability theory and numerous applications. We derive a method
  for construction of upper and lower bounds for probabilities that r from n events occur. We
  use resolutions of those probabilities in sums of positive items and bound them separately.
  This yields new inequalities sharper than earlier ones which correspond to trivial resolutions.
  New inequalities are optimal. There exist examples which show that they may turn to
  equalities. Note that the method will give more sharp bounds when the number of moments increases. But this imply more difficult calculations as well. By the same method, similar
  bounds are obtained for conditional probabilities of corresponding events given a σ-field.
  Here, the accuracy of bounds also increases when one enlarges the numbers of moments
  under consideration. Taking an expectation from both parts of inequalities for conditional
  probabilities, one can derive sharper bounds for unconditional probabilities.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: Работа выполнена при финансовой поддержке РФФИ (проект 18-01-00393).
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 5(63); Issue 3
metadata.lang: -
metadata.name: dc.subject
metadata.value: Bonferroni inequalities
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: probabilities of union of events
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: probabilities of joint occurrence of events
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: On inequalities for probabilities of joint occurrence of several events
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 10-Frolov.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/14889/1/10-Frolov.pdf
resources.format: Adobe PDF
resources.size: 338,67 kB