Power Length-Biased New XLindley Distribution: Properties and Modeling of Real Data
The increasing complexity of modern lifetime data necessitates the development of more flexible probability models. To address this need, we propose the power length-biased new XLindley (PLNXL) distribution, a novel two-parameter model tailored to model a wide range of lifetime datasets. Characteriz...
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MDPI AG
2025-04-01
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| Series: | Mathematics |
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| author | Suresha Kharvi Muhammed Rasheed Irshad Amer Ibrahim Al-Omari Rehab Alsultan |
| author_facet | Suresha Kharvi Muhammed Rasheed Irshad Amer Ibrahim Al-Omari Rehab Alsultan |
| author_sort | Suresha Kharvi |
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| description | The increasing complexity of modern lifetime data necessitates the development of more flexible probability models. To address this need, we propose the power length-biased new XLindley (PLNXL) distribution, a novel two-parameter model tailored to model a wide range of lifetime datasets. Characterized by both shape and scale parameters, the PLNXL distribution effectively captures diverse hazard rate functions, including increasing, decreasing, and inverted bathtub-shaped forms. Additionally, its mean residual life function is capable of exhibiting decreasing, increasing, and bathtub-shaped behaviors, thereby enhancing its practical relevance. We derive key mathematical properties of the distribution, including moments, reliability measures, and entropy. The parameters are estimated using the maximum likelihood method, and simulation studies confirm the consistency and efficiency of the estimators. The applicability of the proposed model is illustrated using real-world datasets, where it consistently outperforms the existing models. These results highlight the robustness and adaptability of the PLNXL distribution for lifetime data analysis across a wide array of applications. |
| format | Article |
| id | doaj-art-71c1a00f1d4d49eb8943bdadd1f2d5a2 |
| institution | OA Journals |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | MDPI AG |
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| series | Mathematics |
| spelling | doaj-art-71c1a00f1d4d49eb8943bdadd1f2d5a22025-08-20T01:49:11ZengMDPI AGMathematics2227-73902025-04-01139139410.3390/math13091394Power Length-Biased New XLindley Distribution: Properties and Modeling of Real DataSuresha Kharvi0Muhammed Rasheed Irshad1Amer Ibrahim Al-Omari2Rehab Alsultan3Department of Biostatistics, KS Hegde Medical Academy, Nitte University, Mangalore 575018, Karnataka, IndiaDepartment of Statistics, Cochin University of Science and Technology, Cochin 682022, Kerala, IndiaDepartment of Mathematics, Faculty of Science, Al Al-Bayt University, Mafraq 25113, JordanMathematics Department, Faculty of Sciences, Umm Al-Qura University, Makkah 21955, Saudi ArabiaThe increasing complexity of modern lifetime data necessitates the development of more flexible probability models. To address this need, we propose the power length-biased new XLindley (PLNXL) distribution, a novel two-parameter model tailored to model a wide range of lifetime datasets. Characterized by both shape and scale parameters, the PLNXL distribution effectively captures diverse hazard rate functions, including increasing, decreasing, and inverted bathtub-shaped forms. Additionally, its mean residual life function is capable of exhibiting decreasing, increasing, and bathtub-shaped behaviors, thereby enhancing its practical relevance. We derive key mathematical properties of the distribution, including moments, reliability measures, and entropy. The parameters are estimated using the maximum likelihood method, and simulation studies confirm the consistency and efficiency of the estimators. The applicability of the proposed model is illustrated using real-world datasets, where it consistently outperforms the existing models. These results highlight the robustness and adaptability of the PLNXL distribution for lifetime data analysis across a wide array of applications.https://www.mdpi.com/2227-7390/13/9/1394lifetime distributionhazard rate functionmean residual life functionmaximum likelihood estimationpower length-biased new XLindley distribution |
| spellingShingle | Suresha Kharvi Muhammed Rasheed Irshad Amer Ibrahim Al-Omari Rehab Alsultan Power Length-Biased New XLindley Distribution: Properties and Modeling of Real Data Mathematics lifetime distribution hazard rate function mean residual life function maximum likelihood estimation power length-biased new XLindley distribution |
| title | Power Length-Biased New XLindley Distribution: Properties and Modeling of Real Data |
| title_full | Power Length-Biased New XLindley Distribution: Properties and Modeling of Real Data |
| title_fullStr | Power Length-Biased New XLindley Distribution: Properties and Modeling of Real Data |
| title_full_unstemmed | Power Length-Biased New XLindley Distribution: Properties and Modeling of Real Data |
| title_short | Power Length-Biased New XLindley Distribution: Properties and Modeling of Real Data |
| title_sort | power length biased new xlindley distribution properties and modeling of real data |
| topic | lifetime distribution hazard rate function mean residual life function maximum likelihood estimation power length-biased new XLindley distribution |
| url | https://www.mdpi.com/2227-7390/13/9/1394 |
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