An approach to distribution of the product of two normal variables
Autor(a) principal: | |
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Data de Publicação: | 2012 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10400.2/14662 |
Resumo: | The distribution of product of two normally distributed variables come from the first part of the XX Century. First works about this issue were [1] and [2] showed that under certain conditions the product could be considered as a normally distributed. A more recent approach is [3] that studied approximation to density function of the product using three methods: numerical integration, Monte Carlo simulation and analytical approximation to the result using the normal distribution. They showed as the inverse variation coefficient µ/σ increases, the distribution of the product of two independent normal variables tends towards a normal distribution. Our study is focused in Ware and Lad approaches. The objective was studying which factors have more influence in the presence of normality for the product of two independent normal variables. We have considered two factors: the inverse of the variation coefficient value µ/σ and the combined ratio (product of the two means divided by standard deviation): (µ1µ2(/σ for two normal variables with the same variance. Our results showed that for low values of the inverse of the variation coefficient (less than 1) normal distribution is not a good approximation for the product. Another one, influence of the combined ratio value is less than influence of the inverse of coefficients of variation value. |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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7160 |
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An approach to distribution of the product of two normal variablesProduct of normally distributed variablesInverse coefficient of variationNumerical integrationMonte Carlo simulationCombined ratioThe distribution of product of two normally distributed variables come from the first part of the XX Century. First works about this issue were [1] and [2] showed that under certain conditions the product could be considered as a normally distributed. A more recent approach is [3] that studied approximation to density function of the product using three methods: numerical integration, Monte Carlo simulation and analytical approximation to the result using the normal distribution. They showed as the inverse variation coefficient µ/σ increases, the distribution of the product of two independent normal variables tends towards a normal distribution. Our study is focused in Ware and Lad approaches. The objective was studying which factors have more influence in the presence of normality for the product of two independent normal variables. We have considered two factors: the inverse of the variation coefficient value µ/σ and the combined ratio (product of the two means divided by standard deviation): (µ1µ2(/σ for two normal variables with the same variance. Our results showed that for low values of the inverse of the variation coefficient (less than 1) normal distribution is not a good approximation for the product. Another one, influence of the combined ratio value is less than influence of the inverse of coefficients of variation value.University of Zielona GoraRepositório AbertoOliveira, AmilcarSeijas-Macias, J. Antonio2023-07-31T10:40:58Z20122012-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.2/14662eng10.7151/dmps.1146info: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:RCAAP2023-11-16T15:47:51Zoai:repositorioaberto.uab.pt:10400.2/14662Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T22:53:26.923221Repositório 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 |
An approach to distribution of the product of two normal variables |
title |
An approach to distribution of the product of two normal variables |
spellingShingle |
An approach to distribution of the product of two normal variables Oliveira, Amilcar Product of normally distributed variables Inverse coefficient of variation Numerical integration Monte Carlo simulation Combined ratio |
title_short |
An approach to distribution of the product of two normal variables |
title_full |
An approach to distribution of the product of two normal variables |
title_fullStr |
An approach to distribution of the product of two normal variables |
title_full_unstemmed |
An approach to distribution of the product of two normal variables |
title_sort |
An approach to distribution of the product of two normal variables |
author |
Oliveira, Amilcar |
author_facet |
Oliveira, Amilcar Seijas-Macias, J. Antonio |
author_role |
author |
author2 |
Seijas-Macias, J. Antonio |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Repositório Aberto |
dc.contributor.author.fl_str_mv |
Oliveira, Amilcar Seijas-Macias, J. Antonio |
dc.subject.por.fl_str_mv |
Product of normally distributed variables Inverse coefficient of variation Numerical integration Monte Carlo simulation Combined ratio |
topic |
Product of normally distributed variables Inverse coefficient of variation Numerical integration Monte Carlo simulation Combined ratio |
description |
The distribution of product of two normally distributed variables come from the first part of the XX Century. First works about this issue were [1] and [2] showed that under certain conditions the product could be considered as a normally distributed. A more recent approach is [3] that studied approximation to density function of the product using three methods: numerical integration, Monte Carlo simulation and analytical approximation to the result using the normal distribution. They showed as the inverse variation coefficient µ/σ increases, the distribution of the product of two independent normal variables tends towards a normal distribution. Our study is focused in Ware and Lad approaches. The objective was studying which factors have more influence in the presence of normality for the product of two independent normal variables. We have considered two factors: the inverse of the variation coefficient value µ/σ and the combined ratio (product of the two means divided by standard deviation): (µ1µ2(/σ for two normal variables with the same variance. Our results showed that for low values of the inverse of the variation coefficient (less than 1) normal distribution is not a good approximation for the product. Another one, influence of the combined ratio value is less than influence of the inverse of coefficients of variation value. |
publishDate |
2012 |
dc.date.none.fl_str_mv |
2012 2012-01-01T00:00:00Z 2023-07-31T10:40:58Z |
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/10400.2/14662 |
url |
http://hdl.handle.net/10400.2/14662 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
10.7151/dmps.1146 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
University of Zielona Gora |
publisher.none.fl_str_mv |
University of Zielona Gora |
dc.source.none.fl_str_mv |
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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1799135130680295424 |