Statistical properties and different methods of estimation of transmuted Rayleigh distribution

This article addresses the various properties and different methods of estimation of the unknown parameters of the Transmuted Rayleigh (TR) distribution from the frequentist point of view. Although, our main focus is on estimation from frequentist point of view,  yet, various mathematical and statis...

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Autores:
Dey, Sanku
Raheem, Enayetur
Mukherjee, Saikat
Tipo de recurso:
Article of journal
Fecha de publicación:
2017
Institución:
Universidad Nacional de Colombia
Repositorio:
Universidad Nacional de Colombia
Idioma:
spa
OAI Identifier:
oai:repositorio.unal.edu.co:unal/66508
Acceso en línea:
https://repositorio.unal.edu.co/handle/unal/66508
http://bdigital.unal.edu.co/67536/
Palabra clave:
51 Matemáticas / Mathematics
31 Colecciones de estadística general / Statistics
Transmuted Rayleigh distribution
Hazard Rate Function
Conditional Moments
Order Statistics
Parameter Estimation
Momentos distributivos
Estadísticas de orden
La estimación de parámetros
Riesgo de tipo de función
Rayleigh transmutada.
Rights
openAccess
License
Atribución-NoComercial 4.0 Internacional
id UNACIONAL2_c0bb03f0b4d07b262b0931a213364efb
oai_identifier_str oai:repositorio.unal.edu.co:unal/66508
network_acronym_str UNACIONAL2
network_name_str Universidad Nacional de Colombia
repository_id_str
dc.title.spa.fl_str_mv Statistical properties and different methods of estimation of transmuted Rayleigh distribution
title Statistical properties and different methods of estimation of transmuted Rayleigh distribution
spellingShingle Statistical properties and different methods of estimation of transmuted Rayleigh distribution
51 Matemáticas / Mathematics
31 Colecciones de estadística general / Statistics
Transmuted Rayleigh distribution
Hazard Rate Function
Conditional Moments
Order Statistics
Parameter Estimation
Momentos distributivos
Estadísticas de orden
La estimación de parámetros
Riesgo de tipo de función
Rayleigh transmutada.
title_short Statistical properties and different methods of estimation of transmuted Rayleigh distribution
title_full Statistical properties and different methods of estimation of transmuted Rayleigh distribution
title_fullStr Statistical properties and different methods of estimation of transmuted Rayleigh distribution
title_full_unstemmed Statistical properties and different methods of estimation of transmuted Rayleigh distribution
title_sort Statistical properties and different methods of estimation of transmuted Rayleigh distribution
dc.creator.fl_str_mv Dey, Sanku
Raheem, Enayetur
Mukherjee, Saikat
dc.contributor.author.spa.fl_str_mv Dey, Sanku
Raheem, Enayetur
Mukherjee, Saikat
dc.subject.ddc.spa.fl_str_mv 51 Matemáticas / Mathematics
31 Colecciones de estadística general / Statistics
topic 51 Matemáticas / Mathematics
31 Colecciones de estadística general / Statistics
Transmuted Rayleigh distribution
Hazard Rate Function
Conditional Moments
Order Statistics
Parameter Estimation
Momentos distributivos
Estadísticas de orden
La estimación de parámetros
Riesgo de tipo de función
Rayleigh transmutada.
dc.subject.proposal.spa.fl_str_mv Transmuted Rayleigh distribution
Hazard Rate Function
Conditional Moments
Order Statistics
Parameter Estimation
Momentos distributivos
Estadísticas de orden
La estimación de parámetros
Riesgo de tipo de función
Rayleigh transmutada.
description This article addresses the various properties and different methods of estimation of the unknown parameters of the Transmuted Rayleigh (TR) distribution from the frequentist point of view. Although, our main focus is on estimation from frequentist point of view,  yet, various mathematical and statistical properties of the TR distribution (such as quantiles, moments, moment generating function, conditional moments,  hazard rate, mean residual lifetime, mean past lifetime,  mean deviation about mean and median, the stochastic ordering,  various entropies, stress-strength parameter  and order statistics) are derived.  We briefly describe different frequentist methods of estimation approaches, namely, maximum likelihood estimators, moments estimators, L-moment estimators, percentile based estimators, least squares estimators, method of maximum product of spacings,  method of Cram\'er-von-Mises, methods of Anderson-Darling and right-tail Anderson-Darling and compare them using extensive numerical simulations. Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation for both small and large samples. Finally, the potentiality of the model is analyzed by means of two real data sets which is further illustrated by obtaining bias and standard error of the estimates and the bootstrap percentile confidence intervals using bootstrap resampling.
publishDate 2017
dc.date.issued.spa.fl_str_mv 2017-01-01
dc.date.accessioned.spa.fl_str_mv 2019-07-03T02:16:02Z
dc.date.available.spa.fl_str_mv 2019-07-03T02:16:02Z
dc.type.spa.fl_str_mv Artículo de revista
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dc.identifier.issn.spa.fl_str_mv ISSN: 2389-8976
dc.identifier.uri.none.fl_str_mv https://repositorio.unal.edu.co/handle/unal/66508
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identifier_str_mv ISSN: 2389-8976
url https://repositorio.unal.edu.co/handle/unal/66508
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dc.language.iso.spa.fl_str_mv spa
language spa
dc.relation.spa.fl_str_mv https://revistas.unal.edu.co/index.php/estad/article/view/56153
dc.relation.ispartof.spa.fl_str_mv Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de Estadística
Revista Colombiana de Estadística
dc.relation.references.spa.fl_str_mv Dey, Sanku and Raheem, Enayetur and Mukherjee, Saikat (2017) Statistical properties and different methods of estimation of transmuted Rayleigh distribution. Revista Colombiana de Estadística, 40 (1). pp. 165-203. ISSN 2389-8976
dc.rights.spa.fl_str_mv Derechos reservados - Universidad Nacional de Colombia
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_abf2
dc.rights.license.spa.fl_str_mv Atribución-NoComercial 4.0 Internacional
dc.rights.uri.spa.fl_str_mv http://creativecommons.org/licenses/by-nc/4.0/
dc.rights.accessrights.spa.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv Atribución-NoComercial 4.0 Internacional
Derechos reservados - Universidad Nacional de Colombia
http://creativecommons.org/licenses/by-nc/4.0/
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.mimetype.spa.fl_str_mv application/pdf
dc.publisher.spa.fl_str_mv Universidad Nacional de Colombia - Sede Bogotá - Facultad de Ciencias - Departamento de Estadística
institution Universidad Nacional de Colombia
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spelling Atribución-NoComercial 4.0 InternacionalDerechos reservados - Universidad Nacional de Colombiahttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Dey, Sanku1537d41c-e2c9-4f6d-9ec7-6edaa1aa773a300Raheem, Enayetur5b1d37ca-2b43-40d8-9172-5d89593e0076300Mukherjee, Saikat046b9067-b5e9-42fd-a99b-92eb6ff919613002019-07-03T02:16:02Z2019-07-03T02:16:02Z2017-01-01ISSN: 2389-8976https://repositorio.unal.edu.co/handle/unal/66508http://bdigital.unal.edu.co/67536/This article addresses the various properties and different methods of estimation of the unknown parameters of the Transmuted Rayleigh (TR) distribution from the frequentist point of view. Although, our main focus is on estimation from frequentist point of view,  yet, various mathematical and statistical properties of the TR distribution (such as quantiles, moments, moment generating function, conditional moments,  hazard rate, mean residual lifetime, mean past lifetime,  mean deviation about mean and median, the stochastic ordering,  various entropies, stress-strength parameter  and order statistics) are derived.  We briefly describe different frequentist methods of estimation approaches, namely, maximum likelihood estimators, moments estimators, L-moment estimators, percentile based estimators, least squares estimators, method of maximum product of spacings,  method of Cram\'er-von-Mises, methods of Anderson-Darling and right-tail Anderson-Darling and compare them using extensive numerical simulations. Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation for both small and large samples. Finally, the potentiality of the model is analyzed by means of two real data sets which is further illustrated by obtaining bias and standard error of the estimates and the bootstrap percentile confidence intervals using bootstrap resampling.Este artículo se aborda las varias propiedades y diferentes métodos para la estimación de los desconocidos parámetros de Transmuted Rayleigh (TR) distribución desde el punto de vista de un frequentist. Aunque la tema principal de este artículo es estimación, varias propiedades matemáticas y estadísticas de TR distribución (como cuantiles, momentos, una función que genera momentos, momentos condicionales, la tasa de peligro, la media vida residual, media vida pasada, la desviación media por media y mediana, organización stochastic, entropías varias, parámetros de tensión-fuerza y estadisticas de orden) están derivadas. Describimos brevemente los diferentes métodos de estimación, como máxima probabilidad, método de momentos, estimacién basada por percentil, mínimos cuadrados, método de máximos productos de espacios, el método de Cramér-von-Mises, los métodos de Anderson-Darling y right-tail Anderson-Darling, y compararlos con extensos estudios de simulaciones. Por último, la potencialidad del modelo está estudiando con dos conjuntos de datos reales. El margen de error, el promedio de error de las estimaciones y el percentage bootstrap de los confianza intervalos estan derivido por bootstrap remuestro.application/pdfspaUniversidad Nacional de Colombia - Sede Bogotá - Facultad de Ciencias - Departamento de Estadísticahttps://revistas.unal.edu.co/index.php/estad/article/view/56153Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de EstadísticaRevista Colombiana de EstadísticaDey, Sanku and Raheem, Enayetur and Mukherjee, Saikat (2017) Statistical properties and different methods of estimation of transmuted Rayleigh distribution. Revista Colombiana de Estadística, 40 (1). pp. 165-203. ISSN 2389-897651 Matemáticas / Mathematics31 Colecciones de estadística general / StatisticsTransmuted Rayleigh distributionHazard Rate FunctionConditional MomentsOrder StatisticsParameter EstimationMomentos distributivosEstadísticas de ordenLa estimación de parámetrosRiesgo de tipo de funciónRayleigh transmutada.Statistical properties and different methods of estimation of transmuted Rayleigh distributionArtículo de revistainfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1http://purl.org/coar/version/c_970fb48d4fbd8a85Texthttp://purl.org/redcol/resource_type/ARTORIGINAL56153-314873-1-PB.pdfapplication/pdf7474863https://repositorio.unal.edu.co/bitstream/unal/66508/1/56153-314873-1-PB.pdf649567c71d02afa09618aba2d8559c00MD51THUMBNAIL56153-314873-1-PB.pdf.jpg56153-314873-1-PB.pdf.jpgGenerated Thumbnailimage/jpeg5264https://repositorio.unal.edu.co/bitstream/unal/66508/2/56153-314873-1-PB.pdf.jpgb666ac48c1b695713bff072ce661999eMD52unal/66508oai:repositorio.unal.edu.co:unal/665082023-05-25 23:03:03.004Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.co