A new modification of the flexible Weibull distribution based on power transformation: Monte Carlo simulation and applications
Statistical modeling is a crucial phase for decision-making and predicting future events. Data arising from engineering-related fields have most often complex structures whose failure rate possesses mixed state behaviors (i.e., non-monotonic shapes). For the data sets whose failure rates are in the...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2023-06-01
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| Series: | Heliyon |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2405844023044468 |
| _version_ | 1797797237957328896 |
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| author | Faridoon Khan Zubair Ahmad Saima K. Khosa Mohammed Ahmed Alomair Abdullah Mohammed Alomair Abdulaziz khalid Alsharidi |
| author_facet | Faridoon Khan Zubair Ahmad Saima K. Khosa Mohammed Ahmed Alomair Abdullah Mohammed Alomair Abdulaziz khalid Alsharidi |
| author_sort | Faridoon Khan |
| collection | DOAJ |
| description | Statistical modeling is a crucial phase for decision-making and predicting future events. Data arising from engineering-related fields have most often complex structures whose failure rate possesses mixed state behaviors (i.e., non-monotonic shapes). For the data sets whose failure rates are in the mixed state, the utilization of the traditional probability models is not a suitable choice. Therefore, searching for more flexible probability models that are capable of adequately describing the mixed state failure data sets is an interesting research topic for researchers. In this paper, we propose and study a new statistical model to achieve the above goal. The proposed model is called a new beta power very flexible Weibull distribution and is capable of capturing five different patterns of the failure rate such as uni-modal, decreasing-increasing-decreasing, bathtub, decreasing, increasing-decreasing-increasing shapes. The estimators of the new beta power very flexible Weibull distribution are obtained using the maximum likelihood method. The evaluation of the estimators is assessed by conducting a simulation study. Finally, the usefulness and applicability of the new beta power very flexible Weibull distribution are shown by analyzing two engineering data sets. Using four information criteria, it is observed that the new beta power very flexible Weibull distribution is the best-suited model for dealing with failure times data sets. |
| first_indexed | 2024-03-13T03:45:10Z |
| format | Article |
| id | doaj.art-fdbcc7c7123f4526a1eab2f1313416d9 |
| institution | Directory Open Access Journal |
| issn | 2405-8440 |
| language | English |
| last_indexed | 2024-03-13T03:45:10Z |
| publishDate | 2023-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Heliyon |
| spelling | doaj.art-fdbcc7c7123f4526a1eab2f1313416d92023-06-23T04:43:18ZengElsevierHeliyon2405-84402023-06-0196e17238A new modification of the flexible Weibull distribution based on power transformation: Monte Carlo simulation and applicationsFaridoon Khan0Zubair Ahmad1Saima K. Khosa2Mohammed Ahmed Alomair3Abdullah Mohammed Alomair4Abdulaziz khalid Alsharidi5Pakistan Institute of Development Economics, Islamabad 44000, PakistanDepartment of Statistics, Quaid-e-Azam University, Islamabad 44000, Pakistan; Corresponding authors.Department of Mathematics and Statistics University of Saskatchewan, Saskatoon, SK, CanadaDepartment of Quantitative Methods, School of Business, King Faisal University, Al-Ahsa 31982, Saudi Arabia; Corresponding authors.Department of Quantitative Methods, School of Business, King Faisal University, Al-Ahsa 31982, Saudi ArabiaDepartment of Mathematics and Statistics, College of Science, King Faisal University, Al Ahsa 31982, Saudi ArabiaStatistical modeling is a crucial phase for decision-making and predicting future events. Data arising from engineering-related fields have most often complex structures whose failure rate possesses mixed state behaviors (i.e., non-monotonic shapes). For the data sets whose failure rates are in the mixed state, the utilization of the traditional probability models is not a suitable choice. Therefore, searching for more flexible probability models that are capable of adequately describing the mixed state failure data sets is an interesting research topic for researchers. In this paper, we propose and study a new statistical model to achieve the above goal. The proposed model is called a new beta power very flexible Weibull distribution and is capable of capturing five different patterns of the failure rate such as uni-modal, decreasing-increasing-decreasing, bathtub, decreasing, increasing-decreasing-increasing shapes. The estimators of the new beta power very flexible Weibull distribution are obtained using the maximum likelihood method. The evaluation of the estimators is assessed by conducting a simulation study. Finally, the usefulness and applicability of the new beta power very flexible Weibull distribution are shown by analyzing two engineering data sets. Using four information criteria, it is observed that the new beta power very flexible Weibull distribution is the best-suited model for dealing with failure times data sets.http://www.sciencedirect.com/science/article/pii/S2405844023044468Weibull distributionFlexible Weibull distributionBeta power transformationEstimationSimulationFailure times data |
| spellingShingle | Faridoon Khan Zubair Ahmad Saima K. Khosa Mohammed Ahmed Alomair Abdullah Mohammed Alomair Abdulaziz khalid Alsharidi A new modification of the flexible Weibull distribution based on power transformation: Monte Carlo simulation and applications Heliyon Weibull distribution Flexible Weibull distribution Beta power transformation Estimation Simulation Failure times data |
| title | A new modification of the flexible Weibull distribution based on power transformation: Monte Carlo simulation and applications |
| title_full | A new modification of the flexible Weibull distribution based on power transformation: Monte Carlo simulation and applications |
| title_fullStr | A new modification of the flexible Weibull distribution based on power transformation: Monte Carlo simulation and applications |
| title_full_unstemmed | A new modification of the flexible Weibull distribution based on power transformation: Monte Carlo simulation and applications |
| title_short | A new modification of the flexible Weibull distribution based on power transformation: Monte Carlo simulation and applications |
| title_sort | new modification of the flexible weibull distribution based on power transformation monte carlo simulation and applications |
| topic | Weibull distribution Flexible Weibull distribution Beta power transformation Estimation Simulation Failure times data |
| url | http://www.sciencedirect.com/science/article/pii/S2405844023044468 |
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