Power Length-Biased New XLindley Distribution: Properties and Modeling of Real Data

Suresha Kharvi, Muhammed Rasheed Irshad, Amer Ibrahim Al-Omari () and Rehab Alsultan
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Suresha Kharvi: Department of Biostatistics, KS Hegde Medical Academy, Nitte University, Mangalore 575018, Karnataka, India
Muhammed Rasheed Irshad: Department of Statistics, Cochin University of Science and Technology, Cochin 682022, Kerala, India
Amer Ibrahim Al-Omari: Department of Mathematics, Faculty of Science, Al Al-Bayt University, Mafraq 25113, Jordan
Rehab Alsultan: Mathematics Department, Faculty of Sciences, Umm Al-Qura University, Makkah 21955, Saudi Arabia

Mathematics, 2025, vol. 13, issue 9, 1-21

Abstract: 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.

Keywords: lifetime distribution; hazard rate function; mean residual life function; maximum likelihood estimation; power length-biased new XLindley distribution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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