Efficient Estimation of Two-Parameter Xgamma Distribution Parameters Using Ranked Set Sampling Design
An efficient method such as ranked set sampling is used for estimating the population parameters when the actual observation measurement is expensive and complicated. In this paper, we consider the problem of estimating the two-parameter xgamma (TPXG) distribution parameters under the ranked set sam...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-09-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/17/3170 |
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| author | Amer Ibrahim Al-Omari SidAhmed Benchiha Ibrahim M. Almanjahie |
| author_facet | Amer Ibrahim Al-Omari SidAhmed Benchiha Ibrahim M. Almanjahie |
| author_sort | Amer Ibrahim Al-Omari |
| collection | DOAJ |
| description | An efficient method such as ranked set sampling is used for estimating the population parameters when the actual observation measurement is expensive and complicated. In this paper, we consider the problem of estimating the two-parameter xgamma (TPXG) distribution parameters under the ranked set sampling as well as the simple random sampling design. Various estimation methods, including the weighted least-square estimator, maximum likelihood estimators, least-square estimator, Cramer–von Mises, the maximum product of spacings estimators, and Anderson–Darling estimators, are considered. A comparison between the ranked set sampling and simple random sampling estimators, with the same number of measurement units, is conducted using a simulation study in terms of the bias, mean squared errors, and efficiency of estimators. The merit of the ranked set sampling estimators is examined using real data of bank customers. The results indicate that estimations using the ranked set sampling method are more efficient than the simple random sampling competitor considered in this study. |
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| format | Article |
| id | doaj.art-d8b78256aba34e84b47ad612d130c694 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T01:33:02Z |
| publishDate | 2022-09-01 |
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| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-d8b78256aba34e84b47ad612d130c6942023-11-23T13:39:42ZengMDPI AGMathematics2227-73902022-09-011017317010.3390/math10173170Efficient Estimation of Two-Parameter Xgamma Distribution Parameters Using Ranked Set Sampling DesignAmer Ibrahim Al-Omari0SidAhmed Benchiha1Ibrahim M. Almanjahie2Department of Mathematics, Faculty of Science, Al al-Bayt University, Mafraq 25113, JordanDepartment of Mathematics, University of Djillali Liabes, BP 89, Sidi Bel Abbes 22000, AlgeriaDepartment of Mathematics, College of Science, King Khalid University, Abha 62529, Saudi ArabiaAn efficient method such as ranked set sampling is used for estimating the population parameters when the actual observation measurement is expensive and complicated. In this paper, we consider the problem of estimating the two-parameter xgamma (TPXG) distribution parameters under the ranked set sampling as well as the simple random sampling design. Various estimation methods, including the weighted least-square estimator, maximum likelihood estimators, least-square estimator, Cramer–von Mises, the maximum product of spacings estimators, and Anderson–Darling estimators, are considered. A comparison between the ranked set sampling and simple random sampling estimators, with the same number of measurement units, is conducted using a simulation study in terms of the bias, mean squared errors, and efficiency of estimators. The merit of the ranked set sampling estimators is examined using real data of bank customers. The results indicate that estimations using the ranked set sampling method are more efficient than the simple random sampling competitor considered in this study.https://www.mdpi.com/2227-7390/10/17/3170simple random samplingxgamma distributionweighted least squaresmethod of maximum product of spacingsranked set sampling |
| spellingShingle | Amer Ibrahim Al-Omari SidAhmed Benchiha Ibrahim M. Almanjahie Efficient Estimation of Two-Parameter Xgamma Distribution Parameters Using Ranked Set Sampling Design Mathematics simple random sampling xgamma distribution weighted least squares method of maximum product of spacings ranked set sampling |
| title | Efficient Estimation of Two-Parameter Xgamma Distribution Parameters Using Ranked Set Sampling Design |
| title_full | Efficient Estimation of Two-Parameter Xgamma Distribution Parameters Using Ranked Set Sampling Design |
| title_fullStr | Efficient Estimation of Two-Parameter Xgamma Distribution Parameters Using Ranked Set Sampling Design |
| title_full_unstemmed | Efficient Estimation of Two-Parameter Xgamma Distribution Parameters Using Ranked Set Sampling Design |
| title_short | Efficient Estimation of Two-Parameter Xgamma Distribution Parameters Using Ranked Set Sampling Design |
| title_sort | efficient estimation of two parameter xgamma distribution parameters using ranked set sampling design |
| topic | simple random sampling xgamma distribution weighted least squares method of maximum product of spacings ranked set sampling |
| url | https://www.mdpi.com/2227-7390/10/17/3170 |
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