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Mean Estimation for Time-Based Surveys Using Memory-Type Logarithmic Estimators

Author

Listed:
  • Shashi Bhushan

    (Department of Statistics, University of Lucknow, Lucknow 226007, India
    These authors contributed equally to this work.)

  • Anoop Kumar

    (Department of Statistics, Amity University, Lucknow 226028, India
    These authors contributed equally to this work.)

  • Amer Ibrahim Al-Omari

    (Department of Mathematics, Faculty of Science, Al al-Bayt University, Mafraq 25113, Jordan
    These authors contributed equally to this work.)

  • Ghadah A. Alomani

    (Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
    These authors contributed equally to this work.)

Abstract

This article examines the issue of population mean estimation utilizing past and present data in the form of an exponentially weighted moving average (EWMA) statistic under simple random sampling (SRS). We suggest memory-type logarithmic estimators and derive their properties, such as mean-square error (MSE) and bias up to a first-order approximation. Using the EWMA statistic, the conventional and novel memory-type estimators are compared. Real and artificial populations are used as examples to illustrate the theoretical findings. According to the empirical findings, memory-type logarithmic estimators are superior to the conventional mean estimator, ratio estimator, product estimator, logarithmic-type estimator, and memory-type ratio and product estimators.

Suggested Citation

  • Shashi Bhushan & Anoop Kumar & Amer Ibrahim Al-Omari & Ghadah A. Alomani, 2023. "Mean Estimation for Time-Based Surveys Using Memory-Type Logarithmic Estimators," Mathematics, MDPI, vol. 11(9), pages 1-14, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:9:p:2125-:d:1137280
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    References listed on IDEAS

    as
    1. Soofia Iftikhar & Alamgir Khalil & Amjad Ali & Tahir Mehmood, 2022. "A Novel and Improved Logarithmic Ratio-Product Type Estimator of Mean in Stratified Random Sampling," Mathematical Problems in Engineering, Hindawi, vol. 2022, pages 1-20, June.
    2. Zaman, Tolga, 2019. "Improvement of modified ratio estimators using robust regression methods," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 627-631.
    3. Ehsan Zamanzade & Xinlei Wang, 2018. "Proportion estimation in ranked set sampling in the presence of tie information," Computational Statistics, Springer, vol. 33(3), pages 1349-1366, September.
    4. Usman Shahzad & Ishfaq Ahmad & Evrim Oral & Muhammad Hanif & Ibrahim Mufrah Almanjahie, 2021. "Estimation of the population mean by successive use of an auxiliary variable in median ranked set sampling," Mathematical Population Studies, Taylor & Francis Journals, vol. 28(3), pages 176-199, July.
    5. Muhammad Noor-ul-Amin, 2021. "Memory type estimators of population mean using exponentially weighted moving averages for time scaled surveys," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 50(12), pages 2747-2758, June.
    6. Bo Bergman & Bengt Klefsjö, 1984. "The Total Time on Test Concept and Its Use in Reliability Theory," Operations Research, INFORMS, vol. 32(3), pages 596-606, June.
    7. Tolga Zaman & Hasan Bulut, 2019. "Modified ratio estimators using robust regression methods," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(8), pages 2039-2048, April.
    8. Javid Shabbir & Shakeel Ahmed & Aamir Sanaullah & Ronald Onyango, 2021. "Measuring Performance of Ratio-Exponential-Log Type General Class of Estimators Using Two Auxiliary Variables," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-12, October.
    9. Tolga Zaman & Emre Dünder & Ahmed Audu & David Anekeya Alilah & Usman Shahzad & Muhammad Hanif, 2021. "Robust Regression-Ratio-Type Estimators of the Mean Utilizing Two Auxiliary Variables: A Simulation Study," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-9, September.
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