Properties and Applications of the Modified Kies–Lomax Distribution with Estimation Methods
The present study introduces a new three-parameter model called the modified Kies–Lomax (MKL) distribution to extend the Lomax distribution and increase its flexibility in modeling real-life data. The MKL distribution, due to its flexibility, provides left-skewed, symmetrical, right-skewed, and reve...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/1944864 |
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| author | Abdelaziz Alsubie |
| author_facet | Abdelaziz Alsubie |
| author_sort | Abdelaziz Alsubie |
| collection | DOAJ |
| description | The present study introduces a new three-parameter model called the modified Kies–Lomax (MKL) distribution to extend the Lomax distribution and increase its flexibility in modeling real-life data. The MKL distribution, due to its flexibility, provides left-skewed, symmetrical, right-skewed, and reversed-J shaped densities and increasing, unimodal, decreasing, and bathtub hazard rate shapes. The MKF density can be expressed as a linear mixture of Lomax densities. Some basic mathematical properties of the MKF model are derived. Its parameters are estimated via six estimation algorithms. We explore their performances using detailed simulation results, and the partial and overall ranks are provided for the measures of absolute biases, mean square errors, and mean relative errors to determine the best estimation method. The results show that the maximum product of spacings and maximum likelihood approaches are recommended to estimate the MKL parameters. Finally, the flexibility of the MKL distribution is checked using two real datasets, showing that it can provide close fit to both datasets as compared with other competing Lomax models. The three-parameter MKL model outperforms some four-parameter and five-parameter rival models. |
| format | Article |
| id | doaj-art-c3550ca7fca640c3a30c80dc87bb569a |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-c3550ca7fca640c3a30c80dc87bb569a2025-02-03T05:59:59ZengWileyJournal of Mathematics2314-47852021-01-01202110.1155/2021/1944864Properties and Applications of the Modified Kies–Lomax Distribution with Estimation MethodsAbdelaziz Alsubie0Department of Basic SciencesThe present study introduces a new three-parameter model called the modified Kies–Lomax (MKL) distribution to extend the Lomax distribution and increase its flexibility in modeling real-life data. The MKL distribution, due to its flexibility, provides left-skewed, symmetrical, right-skewed, and reversed-J shaped densities and increasing, unimodal, decreasing, and bathtub hazard rate shapes. The MKF density can be expressed as a linear mixture of Lomax densities. Some basic mathematical properties of the MKF model are derived. Its parameters are estimated via six estimation algorithms. We explore their performances using detailed simulation results, and the partial and overall ranks are provided for the measures of absolute biases, mean square errors, and mean relative errors to determine the best estimation method. The results show that the maximum product of spacings and maximum likelihood approaches are recommended to estimate the MKL parameters. Finally, the flexibility of the MKL distribution is checked using two real datasets, showing that it can provide close fit to both datasets as compared with other competing Lomax models. The three-parameter MKL model outperforms some four-parameter and five-parameter rival models.http://dx.doi.org/10.1155/2021/1944864 |
| spellingShingle | Abdelaziz Alsubie Properties and Applications of the Modified Kies–Lomax Distribution with Estimation Methods Journal of Mathematics |
| title | Properties and Applications of the Modified Kies–Lomax Distribution with Estimation Methods |
| title_full | Properties and Applications of the Modified Kies–Lomax Distribution with Estimation Methods |
| title_fullStr | Properties and Applications of the Modified Kies–Lomax Distribution with Estimation Methods |
| title_full_unstemmed | Properties and Applications of the Modified Kies–Lomax Distribution with Estimation Methods |
| title_short | Properties and Applications of the Modified Kies–Lomax Distribution with Estimation Methods |
| title_sort | properties and applications of the modified kies lomax distribution with estimation methods |
| url | http://dx.doi.org/10.1155/2021/1944864 |
| work_keys_str_mv | AT abdelazizalsubie propertiesandapplicationsofthemodifiedkieslomaxdistributionwithestimationmethods |