On computing the multivariate poisson probability distribution

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dc.authorid0000-0002-6847-9033
dc.authorid0000-0002-2161-8681
dc.authorid0000-0002-3726-6799
dc.contributor.authorÇekyay, Boraen_US
dc.contributor.authorFrenk, Johannes Bartholomeus Gerardusen_US
dc.contributor.authorJavadi, Sonyaen_US
dc.date.accessioned2023-07-06T13:03:44Z
dc.date.available2023-07-06T13:03:44Z
dc.date.issued2023-06-20
dc.departmentIşık Üniversitesi, Mühendislik ve Doğa Bilimleri Fakültesi, Endüstri Mühendisliği Bölümüen_US
dc.departmentIşık University, Faculty of Engineering and Natural Sciences, Department of Industrial Engineeringen_US
dc.description.abstractWithin the theory of non-negative integer valued multivariate infinitely divisible distributions, the multivariate Poisson distribution plays a key role. As in the univariate case, any non-negative integer valued infinitely divisible multivariate distribution can be approximated by a multivariate distribution belonging to the compound Poisson family. The multivariate Poisson distribution is an important member of this family. In recent years, the multivariate Poisson distributions also has gained practical importance, since they serve as models to describe counting data having a positive covariance structure. However, due to the computational complexity of computing the multivariate Poisson probability mass function (pmf) and its corresponding cumulative distribution function (cdf), their use within these counting models is limited. Since most of the theoretical properties of the multivariate Poisson probability distribution seem already to be known, the main focus of this paper is on proposing more efficient algorithms to compute this pmf. Using a well known property of a Poisson multivariate distributed random vector, we propose in this paper a direct approach to calculate this pmf based on finding all solutions of a system of linear Diophantine equations. This new approach complements an already existing procedure depending on the use of recurrence relations existing for the pmf. We compare our new approach with this already existing approach applied to a slightly different set of recurrence relations which are easier to evaluate. A proof of this new set of recurrence relations is also given. As a result, several algorithms are proposed where some of them are based on the new approach and some use the recurrence relations. To test these algorithms, we provide an extensive analysis in the computational section. Based on the experiments in this section, we conclude that the approach finding all solutions of a set of linear Diophantine equations is computationally more efficient than the approach using the recurrence relations to evaluate the pmf of a multivariate Poisson distributed random vector.en_US
dc.description.versionPublisher's Versionen_US
dc.identifier.citationÇekyay, B., Frenk, J. B. G. & Javadi, S. (2023). On computing the multivariate poisson probability distribution. Methodology and Computing in Applied Probability, 25(3). doi:10.1007/s11009-023-10036-zen_US
dc.identifier.doi10.1007/s11009-023-10036-z
dc.identifier.issn1387-5841
dc.identifier.issn1573-7713
dc.identifier.issue3
dc.identifier.scopus2-s2.0-85162201737
dc.identifier.scopusqualityQ2
dc.identifier.urihttps://hdl.handle.net/11729/5580
dc.identifier.urihttp://dx.doi.org/10.1007/s11009-023-10036-z
dc.identifier.volume25
dc.identifier.wosWOS:001016283500002
dc.identifier.wosqualityQ4
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.indekslendigikaynakScience Citation Index Expanded (SCI-EXPANDED)en_US
dc.institutionauthorJavadi, Sonyaen_US
dc.institutionauthorid0000-0002-3726-6799
dc.language.isoenen_US
dc.peerreviewedYesen_US
dc.publicationstatusPublisheden_US
dc.publisherSpringeren_US
dc.relation.ispartofMethodology and Computing in Applied Probabilityen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectComputational proceduresen_US
dc.subjectDiophantine equationen_US
dc.subjectMultivariate Poisson distributionen_US
dc.subjectRecurrence relationen_US
dc.subjectRegressionen_US
dc.subjectMixturesen_US
dc.titleOn computing the multivariate poisson probability distributionen_US
dc.typeArticleen_US

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