Parameter estimation in the Farlie–Gumbel–Morgenstern bivariate Bilal distribution via multistage ranked set sampling
Ranked set sampling is a well-known and efficient method compared to simple random sampling for estimating population parameters. In this study, we focus on the challenge of estimating the scale parameter of the primary variable $ Z $ using a multistage ranked set sample obtained by ordering the mar...
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AIMS Press
2025-02-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2025098 |
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| author | S. P. Arun M. R. Irshad R. Maya Amer I. Al-Omari Shokrya S. Alshqaq |
| author_facet | S. P. Arun M. R. Irshad R. Maya Amer I. Al-Omari Shokrya S. Alshqaq |
| author_sort | S. P. Arun |
| collection | DOAJ |
| description | Ranked set sampling is a well-known and efficient method compared to simple random sampling for estimating population parameters. In this study, we focus on the challenge of estimating the scale parameter of the primary variable $ Z $ using a multistage ranked set sample obtained by ordering the marginal observations of an auxiliary variable $ W $, where the pair $ (W, Z) $ follows the Farlie–Gumbel–Morgenstern bivariate Bilal distribution. Assuming that the dependence parameter $ \phi $ is known, we introduce the best linear unbiased estimator for the scale parameter of the primary variable, utilizing a multistage ranked set sample. We also compare the efficiency of the proposed estimator with that of the maximum likelihood estimator based on the same number of measured units. It is found that the suggested estimators are more efficient than the classical estimators considered in this study. |
| format | Article |
| id | doaj-art-b1856b734c3c4f7c8b94b10d5cc58811 |
| institution | OA Journals |
| issn | 2473-6988 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-b1856b734c3c4f7c8b94b10d5cc588112025-08-20T02:26:19ZengAIMS PressAIMS Mathematics2473-69882025-02-011022083209710.3934/math.2025098Parameter estimation in the Farlie–Gumbel–Morgenstern bivariate Bilal distribution via multistage ranked set samplingS. P. Arun0M. R. Irshad1R. Maya2Amer I. Al-Omari3Shokrya S. Alshqaq4Kerala University Library, Research Centre, University of Kerala, Thiruvananthapuram 695034, IndiaDepartment of Statistics, Cochin University of Science and Technology, Cochin 682 022, Kerala, India; irshadmr@cusat.ac.in, publicationsofmaya@gmail.comDepartment of Statistics, Cochin University of Science and Technology, Cochin 682 022, Kerala, India; irshadmr@cusat.ac.in, publicationsofmaya@gmail.comDepartment of Mathematics, Faculty of Science, Al al-Bayt University, Mafraq 251113, JordanCollege of Science, Jazan University, P.O.Box. 114, Jazan 45142, Kingdom of Saudi Arabia; salshekak@jazanu.edu.saRanked set sampling is a well-known and efficient method compared to simple random sampling for estimating population parameters. In this study, we focus on the challenge of estimating the scale parameter of the primary variable $ Z $ using a multistage ranked set sample obtained by ordering the marginal observations of an auxiliary variable $ W $, where the pair $ (W, Z) $ follows the Farlie–Gumbel–Morgenstern bivariate Bilal distribution. Assuming that the dependence parameter $ \phi $ is known, we introduce the best linear unbiased estimator for the scale parameter of the primary variable, utilizing a multistage ranked set sample. We also compare the efficiency of the proposed estimator with that of the maximum likelihood estimator based on the same number of measured units. It is found that the suggested estimators are more efficient than the classical estimators considered in this study.https://www.aimspress.com/article/doi/10.3934/math.2025098multistage ranked set samplingfarlie–gumbel–morgenstern bivariate bilal distributionbest linear unbiased estimatorfisher information |
| spellingShingle | S. P. Arun M. R. Irshad R. Maya Amer I. Al-Omari Shokrya S. Alshqaq Parameter estimation in the Farlie–Gumbel–Morgenstern bivariate Bilal distribution via multistage ranked set sampling AIMS Mathematics multistage ranked set sampling farlie–gumbel–morgenstern bivariate bilal distribution best linear unbiased estimator fisher information |
| title | Parameter estimation in the Farlie–Gumbel–Morgenstern bivariate Bilal distribution via multistage ranked set sampling |
| title_full | Parameter estimation in the Farlie–Gumbel–Morgenstern bivariate Bilal distribution via multistage ranked set sampling |
| title_fullStr | Parameter estimation in the Farlie–Gumbel–Morgenstern bivariate Bilal distribution via multistage ranked set sampling |
| title_full_unstemmed | Parameter estimation in the Farlie–Gumbel–Morgenstern bivariate Bilal distribution via multistage ranked set sampling |
| title_short | Parameter estimation in the Farlie–Gumbel–Morgenstern bivariate Bilal distribution via multistage ranked set sampling |
| title_sort | parameter estimation in the farlie gumbel morgenstern bivariate bilal distribution via multistage ranked set sampling |
| topic | multistage ranked set sampling farlie–gumbel–morgenstern bivariate bilal distribution best linear unbiased estimator fisher information |
| url | https://www.aimspress.com/article/doi/10.3934/math.2025098 |
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