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Enhanced Estimation of the Unit Lindley Distribution Parameter via Ranked Set Sampling with Real-Data Application

Author

Listed:
  • Sid Ahmed Benchiha

    (Laboratory of Statistics and Stochastic Processes, University of Djillali Liabes, BP 89, Sidi Bel Abbes 22000, Algeria)

  • Amer Ibrahim Al-Omari

    (Department of Mathematics, Faculty of Science, Al Al-Bayt University, Mafraq 25113, Jordan)

  • Ghadah Alomani

    (Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia)

Abstract

This paper investigates various estimation methods for the parameters of the unit Lindley distribution (U-LD) under both ranked set sampling (RSS) and simple random sampling (SRS) designs. The distribution parameters are estimated using the maximum likelihood estimation, ordinary least squares, weighted least squares, maximum product of spacings, minimum spacing absolute distance, minimum spacing absolute log-distance, minimum spacing square distance, minimum spacing square log-distance, linear-exponential, Anderson–Darling (AD), right-tail AD, left-tail AD, left-tail second-order, Cramér–von Mises, and Kolmogorov–Smirnov. A comprehensive simulation study is conducted to assess the performance of these estimators, ensuring an equal number of measuring units across both designs. Additionally, two real datasets of items failure time and COVID-19 are analyzed to illustrate the practical applicability of the proposed estimation methods. The findings reveal that RSS-based estimators consistently outperform their SRS counterparts in terms of mean squared error, bias, and efficiency across all estimation techniques considered. These results highlight the advantages of using RSS in parameter estimation for the U-LD distribution, making it a preferable choice for improved statistical inference.

Suggested Citation

  • Sid Ahmed Benchiha & Amer Ibrahim Al-Omari & Ghadah Alomani, 2025. "Enhanced Estimation of the Unit Lindley Distribution Parameter via Ranked Set Sampling with Real-Data Application," Mathematics, MDPI, vol. 13(10), pages 1-26, May.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:10:p:1645-:d:1658119
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    References listed on IDEAS

    as
    1. Abdul Haq & Jennifer Brown & Elena Moltchanova & Amer Ibrahim Al-Omari, 2016. "Best linear unbiased and invariant estimation in location-scale families based on double-ranked set sampling," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(1), pages 25-48, January.
    2. Mustafa Ç. Korkmaz & Zehra Sedef Korkmaz, 2023. "The unit log–log distribution: a new unit distribution with alternative quantile regression modeling and educational measurements applications," Journal of Applied Statistics, Taylor & Francis Journals, vol. 50(4), pages 889-908, March.
    3. Saralees Nadarajah & Stephen Chan, 2020. "On moments of the unit Lindley distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 47(5), pages 947-949, April.
    4. M. E. Ghitany & J. Mazucheli & A. F. B. Menezes & F. Alqallaf, 2019. "The unit-inverse Gaussian distribution: A new alternative to two-parameter distributions on the unit interval," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(14), pages 3423-3438, July.
    5. Amer Ibrahim Al-Omari & SidAhmed Benchiha & Ibrahim M. Almanjahie, 2021. "Efficient Estimation of the Generalized Quasi-Lindley Distribution Parameters under Ranked Set Sampling and Applications," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-17, July.
    6. Maryam Khalid & Muhammad Aslam & Ibrahim Almanjahie, 2022. "Bayesian Analysis of 3-Component Unit Lindley Mixture Model with Application to Extreme Observations," Mathematical Problems in Engineering, Hindawi, vol. 2022, pages 1-22, February.
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