DC FieldValueLanguage
dc.contributor.authorPianoforte, Federico-
dc.contributor.authorSchulte, Matthias-
dc.date.accessioned2021-12-21T11:30:15Z-
dc.date.available2021-12-21T11:30:15Z-
dc.date.issued2021-
dc.identifier.citationElectronic Journal of Probability 26 : 149 (2021)de_DE
dc.identifier.issn1083-6489de_DE
dc.identifier.urihttp://hdl.handle.net/11420/11357-
dc.description.abstractThis article compares the distributions of integer-valued random variables and Poisson random variables. It considers the total variation and the Wasserstein distance and provides, in particular, explicit bounds on the pointwise difference between the cumulative distribution functions. Special attention is dedicated to estimating the difference when the cumulative distribution functions are evaluated at 0. This permits to approximate the minimum (or maximum) of a collection of random variables by a suitable random variable in the Kolmogorov distance. The main theoretical results are obtained by combining the Chen-Stein method with size-bias coupling and a generalization of size-bias coupling for integer-valued random variables developed herein. A wide variety of applications are then discussed with a focus on stochastic geometry. In particular, transforms of the minimal circumscribed radius and the maximal inradius of Poisson-Voronoi tessellations as well as the minimal inter-point distance of the points of a Poisson process are considered and bounds for their Kolmogorov distances to extreme value distributions are derived.en
dc.language.isoende_DE
dc.relation.ispartofElectronic journal of probabilityde_DE
dc.subjectChen-Stein methodde_DE
dc.subjectExponential approximationde_DE
dc.subjectExtremesde_DE
dc.subjectPoisson approximationde_DE
dc.subjectPoisson-Voronoi tessellationsde_DE
dc.subjectRunsde_DE
dc.subjectSize-bias couplingde_DE
dc.subjectStochastic geometryde_DE
dc.subjectU-statisticsde_DE
dc.titlePoisson approximation with applications to stochastic geometryde_DE
dc.typeArticlede_DE
dc.type.diniarticle-
dcterms.DCMITypeText-
tuhh.abstract.englishThis article compares the distributions of integer-valued random variables and Poisson random variables. It considers the total variation and the Wasserstein distance and provides, in particular, explicit bounds on the pointwise difference between the cumulative distribution functions. Special attention is dedicated to estimating the difference when the cumulative distribution functions are evaluated at 0. This permits to approximate the minimum (or maximum) of a collection of random variables by a suitable random variable in the Kolmogorov distance. The main theoretical results are obtained by combining the Chen-Stein method with size-bias coupling and a generalization of size-bias coupling for integer-valued random variables developed herein. A wide variety of applications are then discussed with a focus on stochastic geometry. In particular, transforms of the minimal circumscribed radius and the maximal inradius of Poisson-Voronoi tessellations as well as the minimal inter-point distance of the points of a Poisson process are considered and bounds for their Kolmogorov distances to extreme value distributions are derived.de_DE
tuhh.publisher.doi10.1214/21-EJP723-
tuhh.publication.instituteMathematik E-10de_DE
tuhh.type.opus(wissenschaftlicher) Artikel-
dc.type.driverarticle-
dc.type.casraiJournal Article-
tuhh.container.volume26de_DE
dc.identifier.scopus2-s2.0-85120789769-
tuhh.container.articlenumber149de_DE
datacite.resourceTypeJournal Article-
datacite.resourceTypeGeneralText-
item.grantfulltextnone-
item.openairecristypehttp://purl.org/coar/resource_type/c_6501-
item.creatorGNDPianoforte, Federico-
item.creatorGNDSchulte, Matthias-
item.openairetypeArticle-
item.fulltextNo Fulltext-
item.cerifentitytypePublications-
item.creatorOrcidPianoforte, Federico-
item.creatorOrcidSchulte, Matthias-
item.languageiso639-1en-
item.mappedtypeArticle-
crisitem.author.deptMathematik E-10-
crisitem.author.parentorgStudiendekanat Elektrotechnik, Informatik und Mathematik-
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