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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Suresha Kharvi & Muhammed Rasheed Irshad & Amer Ibrahim Al-Omari & Rehab Alsultan, 2025. "Power Length-Biased New XLindley Distribution: Properties and Modeling of Real Data," Mathematics, MDPI, vol. 13(9), pages 1-21, April.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:9:p:1394-:d:1641741
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    References listed on IDEAS

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    1. Deepesh Bhati & Mohd. Malik & H. Vaman, 2015. "Lindley–Exponential distribution: properties and applications," METRON, Springer;Sapienza Università di Roma, vol. 73(3), pages 335-357, December.
    2. Farouk Metiri & Halim Zeghdoudi & Abdelali Ezzebsa, 2022. "On the characterisation of X-Lindley distribution by truncated moments. Properties and application," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 32(1), pages 97-109.
    3. Ghitany, M.E. & Al-Mutairi, D.K. & Balakrishnan, N. & Al-Enezi, L.J., 2013. "Power Lindley distribution and associated inference," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 20-33.
    4. Steve Bennett, 1983. "Log‐Logistic Regression Models for Survival Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 32(2), pages 165-171, June.
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