Estimation of Distribution Function using Percentile Ranked Set Sampling
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://doi.org/10.57805/revstat.v21i1.394 |
Resumo: | The estimation of distribution function has received considerable attention in the literature. Because, many practical problems involve estimation of distribution function from experimental data. Estimating the distribution function makes it possible to do pointwise estimation and to make statistical inference about the distribution of interested population. In this study, we suggested an empirical distribution function (EDF) for percentile ranked set sampling (PRSS). Bias of the EDF estimator is investigated theoretically and numerically. Relative efficiencies of the proposed EDF estimator based on PRSS with respect to EDF estimator based on simple random sampling (SRS) and ranked set sampling (RSS) are obtained. We also considered impact of imperfect rankings on the EDF based on PRSS. According to the results, the proposed EDF estimator is unbiased for the extreme ”minimum and maximum” points and center of the distribution. Also, it is clearly appeared that the EDF estima[1]tor based on PRSS is more efficient than the EDF based on SRS. Another important result is that the suggested EDF estimator has larger efficiencies than the EDF based on RSS for some special cases of PRSS. In the application, the EDF based on PRSS is used to estimate the proportion of women in obesity class III (BMI> 40). |
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Estimation of Distribution Function using Percentile Ranked Set Samplingpercentile ranked set samplingempirical distribution functionrelative efficiencymean squared errorimperfect rankingbody mass index dataThe estimation of distribution function has received considerable attention in the literature. Because, many practical problems involve estimation of distribution function from experimental data. Estimating the distribution function makes it possible to do pointwise estimation and to make statistical inference about the distribution of interested population. In this study, we suggested an empirical distribution function (EDF) for percentile ranked set sampling (PRSS). Bias of the EDF estimator is investigated theoretically and numerically. Relative efficiencies of the proposed EDF estimator based on PRSS with respect to EDF estimator based on simple random sampling (SRS) and ranked set sampling (RSS) are obtained. We also considered impact of imperfect rankings on the EDF based on PRSS. According to the results, the proposed EDF estimator is unbiased for the extreme ”minimum and maximum” points and center of the distribution. Also, it is clearly appeared that the EDF estima[1]tor based on PRSS is more efficient than the EDF based on SRS. Another important result is that the suggested EDF estimator has larger efficiencies than the EDF based on RSS for some special cases of PRSS. In the application, the EDF based on PRSS is used to estimate the proportion of women in obesity class III (BMI> 40).Statistics Portugal2023-05-26info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://doi.org/10.57805/revstat.v21i1.394https://doi.org/10.57805/revstat.v21i1.394REVSTAT-Statistical Journal; Vol. 21 No. 1 (2023): REVSTAT-Statistical Journal; 39-62REVSTAT; Vol. 21 N.º 1 (2023): REVSTAT-Statistical Journal; 39-622183-03711645-6726reponame: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/394https://revstat.ine.pt/index.php/REVSTAT/article/view/394/627Copyright (c) 2021 REVSTAT-Statistical Journalinfo:eu-repo/semantics/openAccessCan Sevil , YusufOzkal Yildiz , Tugba2023-05-27T06:30:13Zoai:revstat:article/394Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T17:56:25.505704Repositório 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 |
Estimation of Distribution Function using Percentile Ranked Set Sampling |
title |
Estimation of Distribution Function using Percentile Ranked Set Sampling |
spellingShingle |
Estimation of Distribution Function using Percentile Ranked Set Sampling Can Sevil , Yusuf percentile ranked set sampling empirical distribution function relative efficiency mean squared error imperfect ranking body mass index data |
title_short |
Estimation of Distribution Function using Percentile Ranked Set Sampling |
title_full |
Estimation of Distribution Function using Percentile Ranked Set Sampling |
title_fullStr |
Estimation of Distribution Function using Percentile Ranked Set Sampling |
title_full_unstemmed |
Estimation of Distribution Function using Percentile Ranked Set Sampling |
title_sort |
Estimation of Distribution Function using Percentile Ranked Set Sampling |
author |
Can Sevil , Yusuf |
author_facet |
Can Sevil , Yusuf Ozkal Yildiz , Tugba |
author_role |
author |
author2 |
Ozkal Yildiz , Tugba |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Can Sevil , Yusuf Ozkal Yildiz , Tugba |
dc.subject.por.fl_str_mv |
percentile ranked set sampling empirical distribution function relative efficiency mean squared error imperfect ranking body mass index data |
topic |
percentile ranked set sampling empirical distribution function relative efficiency mean squared error imperfect ranking body mass index data |
description |
The estimation of distribution function has received considerable attention in the literature. Because, many practical problems involve estimation of distribution function from experimental data. Estimating the distribution function makes it possible to do pointwise estimation and to make statistical inference about the distribution of interested population. In this study, we suggested an empirical distribution function (EDF) for percentile ranked set sampling (PRSS). Bias of the EDF estimator is investigated theoretically and numerically. Relative efficiencies of the proposed EDF estimator based on PRSS with respect to EDF estimator based on simple random sampling (SRS) and ranked set sampling (RSS) are obtained. We also considered impact of imperfect rankings on the EDF based on PRSS. According to the results, the proposed EDF estimator is unbiased for the extreme ”minimum and maximum” points and center of the distribution. Also, it is clearly appeared that the EDF estima[1]tor based on PRSS is more efficient than the EDF based on SRS. Another important result is that the suggested EDF estimator has larger efficiencies than the EDF based on RSS for some special cases of PRSS. In the application, the EDF based on PRSS is used to estimate the proportion of women in obesity class III (BMI> 40). |
publishDate |
2023 |
dc.date.none.fl_str_mv |
2023-05-26 |
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://doi.org/10.57805/revstat.v21i1.394 https://doi.org/10.57805/revstat.v21i1.394 |
url |
https://doi.org/10.57805/revstat.v21i1.394 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
https://revstat.ine.pt/index.php/REVSTAT/article/view/394 https://revstat.ine.pt/index.php/REVSTAT/article/view/394/627 |
dc.rights.driver.fl_str_mv |
Copyright (c) 2021 REVSTAT-Statistical Journal info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
Copyright (c) 2021 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; Vol. 21 No. 1 (2023): REVSTAT-Statistical Journal; 39-62 REVSTAT; Vol. 21 N.º 1 (2023): REVSTAT-Statistical Journal; 39-62 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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1799131638973595648 |