Bimodal and Multimodal Extensions of the Normal and Skew Normal Distributions
Autor(a) principal: | |
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Data de Publicação: | 2023 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | https://revstat.ine.pt/index.php/REVSTAT/article/view/563 |
Resumo: | A transformation of a density function is introduced to derive two families of continuous densities, the first symmetric and the second not-necessarily symmetric, exhibiting both unimodality and bimodality. Their respective density functions are provided in closed form, allowing us to simply obtain moments and related quantities. We focus on the case where the normal distribution is considered, although it can be applied to other models, such as the logistic and Cauchy distributions. This transformation is also extended to derive a family of asymmetric unimodal and bimodal distributions via Azzalini’s scheme. An example related to environmental science illustrate these models’ practical performance. |
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7160 |
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Bimodal and Multimodal Extensions of the Normal and Skew Normal Distributionsmultimodalityold faithful geyser dataskewnessunimodalityunivariate distributionA transformation of a density function is introduced to derive two families of continuous densities, the first symmetric and the second not-necessarily symmetric, exhibiting both unimodality and bimodality. Their respective density functions are provided in closed form, allowing us to simply obtain moments and related quantities. We focus on the case where the normal distribution is considered, although it can be applied to other models, such as the logistic and Cauchy distributions. This transformation is also extended to derive a family of asymmetric unimodal and bimodal distributions via Azzalini’s scheme. An example related to environmental science illustrate these models’ practical performance.Statistics Portugal2023-06-20info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://revstat.ine.pt/index.php/REVSTAT/article/view/563REVSTAT-Statistical Journal; new articleREVSTAT; new article2183-03711645-6726reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAPenghttps://revstat.ine.pt/index.php/REVSTAT/article/view/563https://revstat.ine.pt/index.php/REVSTAT/article/view/563/635Copyright (c) 2022 REVSTAT-Statistical Journalinfo:eu-repo/semantics/openAccessGómez-Déniz, EmilioCalderín-Ojeda, EnriqueM. Sarabia, José2023-06-24T06:30:22Zoai:revstat:article/563Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T18:01:26.866156Repositório 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 |
Bimodal and Multimodal Extensions of the Normal and Skew Normal Distributions |
title |
Bimodal and Multimodal Extensions of the Normal and Skew Normal Distributions |
spellingShingle |
Bimodal and Multimodal Extensions of the Normal and Skew Normal Distributions Gómez-Déniz, Emilio multimodality old faithful geyser data skewness unimodality univariate distribution |
title_short |
Bimodal and Multimodal Extensions of the Normal and Skew Normal Distributions |
title_full |
Bimodal and Multimodal Extensions of the Normal and Skew Normal Distributions |
title_fullStr |
Bimodal and Multimodal Extensions of the Normal and Skew Normal Distributions |
title_full_unstemmed |
Bimodal and Multimodal Extensions of the Normal and Skew Normal Distributions |
title_sort |
Bimodal and Multimodal Extensions of the Normal and Skew Normal Distributions |
author |
Gómez-Déniz, Emilio |
author_facet |
Gómez-Déniz, Emilio Calderín-Ojeda, Enrique M. Sarabia, José |
author_role |
author |
author2 |
Calderín-Ojeda, Enrique M. Sarabia, José |
author2_role |
author author |
dc.contributor.author.fl_str_mv |
Gómez-Déniz, Emilio Calderín-Ojeda, Enrique M. Sarabia, José |
dc.subject.por.fl_str_mv |
multimodality old faithful geyser data skewness unimodality univariate distribution |
topic |
multimodality old faithful geyser data skewness unimodality univariate distribution |
description |
A transformation of a density function is introduced to derive two families of continuous densities, the first symmetric and the second not-necessarily symmetric, exhibiting both unimodality and bimodality. Their respective density functions are provided in closed form, allowing us to simply obtain moments and related quantities. We focus on the case where the normal distribution is considered, although it can be applied to other models, such as the logistic and Cauchy distributions. This transformation is also extended to derive a family of asymmetric unimodal and bimodal distributions via Azzalini’s scheme. An example related to environmental science illustrate these models’ practical performance. |
publishDate |
2023 |
dc.date.none.fl_str_mv |
2023-06-20 |
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 |
https://revstat.ine.pt/index.php/REVSTAT/article/view/563 |
url |
https://revstat.ine.pt/index.php/REVSTAT/article/view/563 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
https://revstat.ine.pt/index.php/REVSTAT/article/view/563 https://revstat.ine.pt/index.php/REVSTAT/article/view/563/635 |
dc.rights.driver.fl_str_mv |
Copyright (c) 2022 REVSTAT-Statistical Journal info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
Copyright (c) 2022 REVSTAT-Statistical Journal |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Statistics Portugal |
publisher.none.fl_str_mv |
Statistics Portugal |
dc.source.none.fl_str_mv |
REVSTAT-Statistical Journal; new article REVSTAT; new article 2183-0371 1645-6726 reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
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 |
repository.mail.fl_str_mv |
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1799131681854062592 |