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Estimation of distribution function using L ranked set sampling and robust extreme ranked set sampling with application to reliability

Author

Listed:
  • Mohamed S. Abdallah

    (Aswan University)

  • Amer I. Al-Omari

    (Al al-Bayt University)

  • Naif Alotaibi

    (Imam Mohammad Ibn Saud, Islamic University)

  • Ghadah A. Alomani

    (Princess Nourah bint Abdulrahman University)

  • A. S. Al-Moisheer

    (Jouf University)

Abstract

This paper suggests new estimators for cumulative distribution function (CDF) using L ranked set sampling (LRSS) and robust extreme ranked set sampling (RERSS) methods. The proposed estimators are deduced based on maximum likelihood estimation method and its asymptotic properties are theoretically investigated. Comparison study has been made to demonstrate the efficiency of the proposed estimators. It is found that when the data contain outliers, the proposed estimators are less sensitive and have a satisfied behavior compared to their analog in ranked set sampling as the population CDF is far away from the boundaries. Motivated by this efficiency gain, we provided new estimators for system reliability $$\mathcal{R}$$ R = $$P(Y>X)$$ P ( Y > X ) using LRSS and RERSS. Through a Monte Carlo simulation study, the performance of the introduced reliability estimators is also examined. A real data set is analyzed to illustrate the applicability of the proposed various estimators.

Suggested Citation

  • Mohamed S. Abdallah & Amer I. Al-Omari & Naif Alotaibi & Ghadah A. Alomani & A. S. Al-Moisheer, 2022. "Estimation of distribution function using L ranked set sampling and robust extreme ranked set sampling with application to reliability," Computational Statistics, Springer, vol. 37(5), pages 2333-2362, November.
    • Handle: RePEc:spr:compst:v:37:y:2022:i:5:d:10.1007_s00180-022-01201-y
    DOI: 10.1007/s00180-022-01201-y
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    References listed on IDEAS

    as
    1. Zamanzade, Ehsan & Mahdizadeh, M., 2017. "A more efficient proportion estimator in ranked set sampling," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 28-33.
    2. M. Mahdizadeh & Ehsan Zamanzade, 2018. "Stratified pair ranked set sampling," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(24), pages 5904-5915, December.
    3. Ehsan Zamanzade, 2019. "EDF-based tests of exponentiality in pair ranked set sampling," Statistical Papers, Springer, vol. 60(6), pages 2141-2159, December.
    4. Sanku Dey & Mahdi Salehi & Jafar Ahmadi, 2017. "Rayleigh distribution revisited via ranked set sampling," METRON, Springer;Sapienza Università di Roma, vol. 75(1), pages 69-85, April.
    5. Ehsan Zamanzade & M. Mahdizadeh & Hani M. Samawi, 2020. "Efficient estimation of cumulative distribution function using moving extreme ranked set sampling with application to reliability," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(3), pages 485-502, September.
    6. Omer Ozturk, 2010. "Nonparametric maximum-likelihood estimation of within-set ranking errors in ranked set sampling," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(7), pages 823-840.
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