A DeMoivre-Laplace theorem of all orders of regularity

Detalhes bibliográficos
Autor(a) principal: van den Berg, Imme
Data de Publicação: 2007
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10174/1396
Resumo: The DeMoivre-Laplace Theorem states that the binomial probability distribution B(N; 1/2) tends for N to infinity to the Gaussian distribution. We extend this theorem to the difference quotients of the family of the binomial distributions with varying N, showing that they converge to the corresponding differential quotients of the time-dependent Gaussian distribution. The convergence holds for difference quotients of all order.
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spelling A DeMoivre-Laplace theorem of all orders of regularityBinomial distributionDeMoivre-Laplace TheoremPascal TriangleGaussian distributiondifference quotientsdiscrete heat equationnonstandard analysisThe DeMoivre-Laplace Theorem states that the binomial probability distribution B(N; 1/2) tends for N to infinity to the Gaussian distribution. We extend this theorem to the difference quotients of the family of the binomial distributions with varying N, showing that they converge to the corresponding differential quotients of the time-dependent Gaussian distribution. The convergence holds for difference quotients of all order.Shaker Publishing, Maastricht/Aachen2008-12-30T16:26:21Z2008-12-302007-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article30216 bytesapplication/pdfhttp://hdl.handle.net/10174/1396http://hdl.handle.net/10174/1396engp. 335-360livreivdb@uevora.ptCommunications of the Laufen Colloquium on Science 2007, A. Ruffing, A. Suhrer, J. Suhrer (Eds.)340van den Berg, Immeinfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-01-03T18:37:29Zoai:dspace.uevora.pt:10174/1396Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T00:57:32.564998Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv A DeMoivre-Laplace theorem of all orders of regularity
title A DeMoivre-Laplace theorem of all orders of regularity
spellingShingle A DeMoivre-Laplace theorem of all orders of regularity
van den Berg, Imme
Binomial distribution
DeMoivre-Laplace Theorem
Pascal Triangle
Gaussian distribution
difference quotients
discrete heat equation
nonstandard analysis
title_short A DeMoivre-Laplace theorem of all orders of regularity
title_full A DeMoivre-Laplace theorem of all orders of regularity
title_fullStr A DeMoivre-Laplace theorem of all orders of regularity
title_full_unstemmed A DeMoivre-Laplace theorem of all orders of regularity
title_sort A DeMoivre-Laplace theorem of all orders of regularity
author van den Berg, Imme
author_facet van den Berg, Imme
author_role author
dc.contributor.author.fl_str_mv van den Berg, Imme
dc.subject.por.fl_str_mv Binomial distribution
DeMoivre-Laplace Theorem
Pascal Triangle
Gaussian distribution
difference quotients
discrete heat equation
nonstandard analysis
topic Binomial distribution
DeMoivre-Laplace Theorem
Pascal Triangle
Gaussian distribution
difference quotients
discrete heat equation
nonstandard analysis
description The DeMoivre-Laplace Theorem states that the binomial probability distribution B(N; 1/2) tends for N to infinity to the Gaussian distribution. We extend this theorem to the difference quotients of the family of the binomial distributions with varying N, showing that they converge to the corresponding differential quotients of the time-dependent Gaussian distribution. The convergence holds for difference quotients of all order.
publishDate 2007
dc.date.none.fl_str_mv 2007-01-01T00:00:00Z
2008-12-30T16:26:21Z
2008-12-30
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10174/1396
http://hdl.handle.net/10174/1396
url http://hdl.handle.net/10174/1396
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv p. 335-360
livre
ivdb@uevora.pt
Communications of the Laufen Colloquium on Science 2007, A. Ruffing, A. Suhrer, J. Suhrer (Eds.)
340
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 30216 bytes
application/pdf
dc.publisher.none.fl_str_mv Shaker Publishing, Maastricht/Aachen
publisher.none.fl_str_mv Shaker Publishing, Maastricht/Aachen
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
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instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
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reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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