Estimation of Distribution Function using Percentile Ranked Set Sampling
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 statistic...
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| Format: | Article |
| Language: | English |
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Instituto Nacional de Estatística | Statistics Portugal
2023-05-01
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| Series: | Revstat Statistical Journal |
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| Online Access: | https://revstat.ine.pt/index.php/REVSTAT/article/view/394 |
| _version_ | 1797818856242151424 |
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| author | Yusuf Can Sevil Tugba Ozkal Yildiz |
| author_facet | Yusuf Can Sevil Tugba Ozkal Yildiz |
| author_sort | Yusuf Can Sevil |
| collection | DOAJ |
| 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).
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| first_indexed | 2024-03-13T09:15:17Z |
| format | Article |
| id | doaj.art-8bff14f969414248986c8892cc424fd1 |
| institution | Directory Open Access Journal |
| issn | 1645-6726 2183-0371 |
| language | English |
| last_indexed | 2024-03-13T09:15:17Z |
| publishDate | 2023-05-01 |
| publisher | Instituto Nacional de Estatística | Statistics Portugal |
| record_format | Article |
| series | Revstat Statistical Journal |
| spelling | doaj.art-8bff14f969414248986c8892cc424fd12023-05-26T10:48:52ZengInstituto Nacional de Estatística | Statistics PortugalRevstat Statistical Journal1645-67262183-03712023-05-0121110.57805/revstat.v21i1.394Estimation of Distribution Function using Percentile Ranked Set SamplingYusuf Can Sevil 0Tugba Ozkal Yildiz 1Dokuz Eylul UniversityDokuz Eylul University 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). https://revstat.ine.pt/index.php/REVSTAT/article/view/394percentile ranked set samplingempirical distribution functionrelative efficiencymean squared errorimperfect rankingbody mass index data |
| spellingShingle | Yusuf Can Sevil Tugba Ozkal Yildiz Estimation of Distribution Function using Percentile Ranked Set Sampling Revstat Statistical Journal percentile ranked set sampling empirical distribution function relative efficiency mean squared error imperfect ranking body mass index data |
| title | 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_short | Estimation of Distribution Function using Percentile Ranked Set Sampling |
| title_sort | estimation of distribution function using percentile ranked set sampling |
| topic | percentile ranked set sampling empirical distribution function relative efficiency mean squared error imperfect ranking body mass index data |
| url | https://revstat.ine.pt/index.php/REVSTAT/article/view/394 |
| work_keys_str_mv | AT yusufcansevil estimationofdistributionfunctionusingpercentilerankedsetsampling AT tugbaozkalyildiz estimationofdistributionfunctionusingpercentilerankedsetsampling |