Robust Reliability Estimation for Lindley Distribution—A Probability Integral Transform Statistical Approach
In the modeling and analysis of reliability data via the Lindley distribution, the maximum likelihood estimator is the most commonly used for parameter estimation. However, the maximum likelihood estimator is highly sensitive to the presence of outliers. In this paper, based on the probability integ...
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| Format: | Article |
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MDPI AG
2020-09-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/9/1634 |
| _version_ | 1797553117108109312 |
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| author | Muhammad Aslam Mohd Safari Nurulkamal Masseran Muhammad Hilmi Abdul Majid |
| author_facet | Muhammad Aslam Mohd Safari Nurulkamal Masseran Muhammad Hilmi Abdul Majid |
| author_sort | Muhammad Aslam Mohd Safari |
| collection | DOAJ |
| description | In the modeling and analysis of reliability data via the Lindley distribution, the maximum likelihood estimator is the most commonly used for parameter estimation. However, the maximum likelihood estimator is highly sensitive to the presence of outliers. In this paper, based on the probability integral transform statistic, a robust and efficient estimator of the parameter of the Lindley distribution is proposed. We investigate the relative efficiency of the new estimator compared to that of the maximum likelihood estimator, as well as its robustness based on the breakdown point and influence function. It is found that this new estimator provides reasonable protection against outliers while also being simple to compute. Using a Monte Carlo simulation, we compare the performance of the new estimator and several well-known methods, including the maximum likelihood, ordinary least-squares and weighted least-squares methods in the absence and presence of outliers. The results reveal that the new estimator is highly competitive with the maximum likelihood estimator in the absence of outliers and outperforms the other methods in the presence of outliers. Finally, we conduct a statistical analysis of four reliability data sets, the results of which support the simulation results. |
| first_indexed | 2024-03-10T16:10:52Z |
| format | Article |
| id | doaj.art-9d49ef0065914082a7bf193ece2ec0c0 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T16:10:52Z |
| publishDate | 2020-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-9d49ef0065914082a7bf193ece2ec0c02023-11-20T14:30:16ZengMDPI AGMathematics2227-73902020-09-0189163410.3390/math8091634Robust Reliability Estimation for Lindley Distribution—A Probability Integral Transform Statistical ApproachMuhammad Aslam Mohd Safari0Nurulkamal Masseran1Muhammad Hilmi Abdul Majid2Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi 43600, Selangor, MalaysiaDepartment of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi 43600, Selangor, MalaysiaDepartment of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi 43600, Selangor, MalaysiaIn the modeling and analysis of reliability data via the Lindley distribution, the maximum likelihood estimator is the most commonly used for parameter estimation. However, the maximum likelihood estimator is highly sensitive to the presence of outliers. In this paper, based on the probability integral transform statistic, a robust and efficient estimator of the parameter of the Lindley distribution is proposed. We investigate the relative efficiency of the new estimator compared to that of the maximum likelihood estimator, as well as its robustness based on the breakdown point and influence function. It is found that this new estimator provides reasonable protection against outliers while also being simple to compute. Using a Monte Carlo simulation, we compare the performance of the new estimator and several well-known methods, including the maximum likelihood, ordinary least-squares and weighted least-squares methods in the absence and presence of outliers. The results reveal that the new estimator is highly competitive with the maximum likelihood estimator in the absence of outliers and outperforms the other methods in the presence of outliers. Finally, we conduct a statistical analysis of four reliability data sets, the results of which support the simulation results.https://www.mdpi.com/2227-7390/8/9/1634Lindley distributionM-estimatorprobability integral transform statisticreliabilityrobust estimation |
| spellingShingle | Muhammad Aslam Mohd Safari Nurulkamal Masseran Muhammad Hilmi Abdul Majid Robust Reliability Estimation for Lindley Distribution—A Probability Integral Transform Statistical Approach Mathematics Lindley distribution M-estimator probability integral transform statistic reliability robust estimation |
| title | Robust Reliability Estimation for Lindley Distribution—A Probability Integral Transform Statistical Approach |
| title_full | Robust Reliability Estimation for Lindley Distribution—A Probability Integral Transform Statistical Approach |
| title_fullStr | Robust Reliability Estimation for Lindley Distribution—A Probability Integral Transform Statistical Approach |
| title_full_unstemmed | Robust Reliability Estimation for Lindley Distribution—A Probability Integral Transform Statistical Approach |
| title_short | Robust Reliability Estimation for Lindley Distribution—A Probability Integral Transform Statistical Approach |
| title_sort | robust reliability estimation for lindley distribution a probability integral transform statistical approach |
| topic | Lindley distribution M-estimator probability integral transform statistic reliability robust estimation |
| url | https://www.mdpi.com/2227-7390/8/9/1634 |
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