Maximum likelihood estimator of the shape parameter under simple random sampling and moving extremes ranked set sampling
This paper examines the maximum likelihood estimator (MLE) for the shape parameter from the shape family, focusing on both simple random sampling (SRS) and moving extremes ranked set sampling (MERSS). The study establishes the existence and uniqueness of the MLE for several common shape distribution...
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| Published in | Statistics & probability letters Vol. 226; p. 110465 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier B.V
01.11.2025
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0167-7152 |
| DOI | 10.1016/j.spl.2025.110465 |
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| Abstract | This paper examines the maximum likelihood estimator (MLE) for the shape parameter from the shape family, focusing on both simple random sampling (SRS) and moving extremes ranked set sampling (MERSS). The study establishes the existence and uniqueness of the MLE for several common shape distributions. In order to give more insight into the performance of MERSS with respect to (w.r.t.) SRS, the asymptotic efficiency of the MLE using MERSS w.r.t. that using SRS is computed for the common shape distributions. The findings from the common shape distributions indicate that MERSS provides a more efficient approach for estimating the shape parameter compared to SRS. Additionally, we examine the implications of imperfect ranking. |
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| AbstractList | This paper examines the maximum likelihood estimator (MLE) for the shape parameter from the shape family, focusing on both simple random sampling (SRS) and moving extremes ranked set sampling (MERSS). The study establishes the existence and uniqueness of the MLE for several common shape distributions. In order to give more insight into the performance of MERSS with respect to (w.r.t.) SRS, the asymptotic efficiency of the MLE using MERSS w.r.t. that using SRS is computed for the common shape distributions. The findings from the common shape distributions indicate that MERSS provides a more efficient approach for estimating the shape parameter compared to SRS. Additionally, we examine the implications of imperfect ranking. |
| ArticleNumber | 110465 |
| Author | Yang, Rui Chen, Wangxue |
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| Cites_doi | 10.1016/j.jkss.2015.06.001 10.1007/s00362-017-0913-9 10.1007/s10182-020-00368-3 10.1080/03610926.2019.1678640 10.1016/j.spl.2013.05.015 10.1007/s00362-018-1011-3 10.1016/j.jkss.2018.08.008 10.1007/s00362-019-01132-9 10.1016/j.spl.2012.07.001 10.1080/00949655.2015.1109097 10.1007/s00362-003-0161-z 10.1080/00949655.2014.958085 10.1080/00949655.2012.662684 10.1080/03610926.2019.1691735 10.1080/03610926.2017.1348519 10.1080/03610918.2013.826364 10.1071/AR9520385 10.1007/BF02911622 10.1007/s11766-021-3720-y 10.1002/env.610 10.1016/j.spl.2016.09.016 10.1080/16843703.2013.11673417 |
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| Keywords | Maximum likelihood estimator Shape parameter 62F10 Fisher information number 62D05 Moving extremes ranked set sampling |
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| References | Dong, Zhang (b10) 2020; 49 Chen, Bai, Sinha (b7) 2003 Zamanzade (b24) 2019; 60 McCool (b15) 2012 Qiu (b17) 2017; 120 Zamanzade (b22) 2015; 85 Al-Omari, Haq (b3) 2015; 86 He, Chen, Qian (b13) 2020; 61 Chen, Xie, Wu (b8) 2013; 83 Qiu, Eftekharian (b19) 2021; 50 Al-Saleh, Al-Hadhrami (b6) 2003; 44 McIntyre (b16) 1952; 3 Al-Omari (b2) 2012; 82 Zamanzade, Mahdizadeh, Samawi (b25) 2020; 104 Al-Odat, Al-Saleh (b1) 2001; 10 Qiu (b18) 2018; 47 Dong, Zhang, Li (b11) 2013; 10 Takahasi, Wakimoto (b21) 1968; 20 Rinne (b20) 2009 Zhang, Dong, Xu (b26) 2014; 43 Al-Saleh, Al-Hadhrami (b5) 2003; 14 Frey, Zhang (b12) 2019; 48 Zamanzade (b23) 2016; 45 He, Chen, Yang (b14) 2021; 36 Al-Omari, Raqab (b4) 2012; 83 Chen, Yang, Yao, Long (b9) 2021; 62 McIntyre (10.1016/j.spl.2025.110465_b16) 1952; 3 Al-Odat (10.1016/j.spl.2025.110465_b1) 2001; 10 Zamanzade (10.1016/j.spl.2025.110465_b23) 2016; 45 Zhang (10.1016/j.spl.2025.110465_b26) 2014; 43 He (10.1016/j.spl.2025.110465_b14) 2021; 36 Takahasi (10.1016/j.spl.2025.110465_b21) 1968; 20 Al-Omari (10.1016/j.spl.2025.110465_b3) 2015; 86 Al-Omari (10.1016/j.spl.2025.110465_b2) 2012; 82 Dong (10.1016/j.spl.2025.110465_b10) 2020; 49 Chen (10.1016/j.spl.2025.110465_b9) 2021; 62 Al-Omari (10.1016/j.spl.2025.110465_b4) 2012; 83 McCool (10.1016/j.spl.2025.110465_b15) 2012 Al-Saleh (10.1016/j.spl.2025.110465_b6) 2003; 44 Qiu (10.1016/j.spl.2025.110465_b18) 2018; 47 Rinne (10.1016/j.spl.2025.110465_b20) 2009 Al-Saleh (10.1016/j.spl.2025.110465_b5) 2003; 14 Zamanzade (10.1016/j.spl.2025.110465_b24) 2019; 60 Zamanzade (10.1016/j.spl.2025.110465_b22) 2015; 85 He (10.1016/j.spl.2025.110465_b13) 2020; 61 Qiu (10.1016/j.spl.2025.110465_b17) 2017; 120 Zamanzade (10.1016/j.spl.2025.110465_b25) 2020; 104 Frey (10.1016/j.spl.2025.110465_b12) 2019; 48 Chen (10.1016/j.spl.2025.110465_b7) 2003 Dong (10.1016/j.spl.2025.110465_b11) 2013; 10 Qiu (10.1016/j.spl.2025.110465_b19) 2021; 50 Chen (10.1016/j.spl.2025.110465_b8) 2013; 83 |
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| Title | Maximum likelihood estimator of the shape parameter under simple random sampling and moving extremes ranked set sampling |
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