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Efficient estimation of cumulative distribution function using moving extreme ranked set sampling with application to reliability

Author

Listed:
  • Ehsan Zamanzade

    (University of Isfahan)

  • M. Mahdizadeh

    (Hakim Sabzevari University)

  • Hani M. Samawi

    (Georgia Southern University)

Abstract

In this article, we consider the problem of estimating cumulative distribution function (CDF) and a reliability parameter using moving extreme ranked set sampling (MERSS). Two different CDF estimators are described and compared with their competitors in simple random sampling (SRS) and ranked set sampling (RSS). It turns out the CDF estimators in MERSS can be more efficient than their competitors in SRS and RSS at a point in a particular tail of the distribution when the quality of rankings is sufficiently good. Motivated by this efficiency gain, we develop some estimators for the stress-strength probability using MERSS. The suggested estimators are then compared with their counterparts in the literature via Monte Carlo simulation. Finally, a real dataset is used to show the applicability of the developed procedures.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:alstar:v:104:y:2020:i:3:d:10.1007_s10182-020-00368-3
    DOI: 10.1007/s10182-020-00368-3
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    References listed on IDEAS

    as
    1. Hani M. Samawi & Lili Yu & Haresh Rochani & Robert Vogel, 2020. "Reducing sample size needed for cox-proportional hazards model analysis using more efficient sampling method," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(6), pages 1281-1298, March.
    2. Mohammad Al-Saleh & Ahmad Al-Ananbeh, 2007. "Estimation of the means of the bivariate normal using moving extreme ranked set sampling with concomitant variable," Statistical Papers, Springer, vol. 48(2), pages 179-195, April.
    3. Walid Abu-Dayyeh & Esam Al Sawi, 2009. "Modified inference about the mean of the exponential distribution using moving extreme ranked set sampling," Statistical Papers, Springer, vol. 50(2), pages 249-259, March.
    4. Fligner, Michael A. & MacEachern, Steven N., 2006. "Nonparametric Two-Sample Methods for Ranked-Set Sample Data," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1107-1118, September.
    5. Hani M. Samawi & Haresh Rochani & Daniel Linder & Arpita Chatterjee, 2017. "More efficient logistic analysis using moving extreme ranked set sampling," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(4), pages 753-766, March.
    6. Omer Ozturk & N. Balakrishnan, 2009. "An Exact Control-Versus-Treatment Comparison Test Based on Ranked Set Samples," Biometrics, The International Biometric Society, vol. 65(4), pages 1213-1222, December.
    7. Zamanzade, Ehsan & Wang, Xinlei, 2017. "Estimation of population proportion for judgment post-stratification," Computational Statistics & Data Analysis, Elsevier, vol. 112(C), pages 257-269.
    8. Mohammad Al-Saleh & Said Al-Hadhrami, 2003. "Estimation of the mean of the exponential distribution using moving extremes ranked set sampling," Statistical Papers, Springer, vol. 44(3), pages 367-382, July.
    9. Lutz Dümbgen & Ehsan Zamanzade, 2020. "Inference on a distribution function from ranked set samples," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(1), pages 157-185, February.
    10. Ehsan Zamanzade & M. Mahdizadeh, 2018. "Estimating the population proportion in pair ranked set sampling with application to air quality monitoring," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(3), pages 426-437, February.
    11. Zamanzade, Ehsan & Mahdizadeh, M., 2017. "A more efficient proportion estimator in ranked set sampling," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 28-33.
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    Cited by:

    1. 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.
    2. Ying Zhou & Liang Wang & Tzong-Ru Tsai & Yogesh Mani Tripathi, 2023. "Estimation of Dependent Competing Risks Model with Baseline Proportional Hazards Models under Minimum Ranked Set Sampling," Mathematics, MDPI, vol. 11(6), pages 1-30, March.

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