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An Efficient Ratio-Cum-Exponential Estimator for Estimating the Population Distribution Function in the Existence of Non-Response Using an SRS Design

Author

Listed:
  • Ayesha Khalid

    (Department of Statistics, COMSATS University Islamabad, Lahore Campus, Islamabad 45550, Pakistan)

  • Aamir Sanaullah

    (Department of Statistics, COMSATS University Islamabad, Lahore Campus, Islamabad 45550, Pakistan)

  • Mohammed M. A. Almazah

    (Department of Mathematics, College of Science and Arts (Muhyil), King Khalid University, Muhyil 61421, Saudi Arabia
    Department of Mathematics and Computer, College of Sciences, Ibb University, Ibb 70270, Yemen)

  • Fuad S. Al-Duais

    (Mathematics Department, College of Humanities and Science, Prince Sattam Bin Abudulaziz University, Al Aflaj 16278, Saudia Arabia
    Administrative Department, Administrative Science College, Thamar University, Thamar 87246, Yemen)

Abstract

To gain insight into various phenomena of interest, cumulative distribution functions (CDFs) can be used to analyze survey data. The purpose of this study was to present an efficient ratiocum-exponential estimator for estimating a population CDF using auxiliary information under two scenarios of non-response. Up to first-order approximation, expressions for the bias and mean squared error (MSE) were derived. The proposed estimator was compared theoretically and empirically, with the modified estimators. The proposed estimator was found to be better than the modified estimators based on present-relative efficiency PRE and MSE criteria under the specific conditions.

Suggested Citation

  • Ayesha Khalid & Aamir Sanaullah & Mohammed M. A. Almazah & Fuad S. Al-Duais, 2023. "An Efficient Ratio-Cum-Exponential Estimator for Estimating the Population Distribution Function in the Existence of Non-Response Using an SRS Design," Mathematics, MDPI, vol. 11(6), pages 1-15, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:6:p:1312-:d:1091673
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    References listed on IDEAS

    as
    1. Abdul Haq & Manzoor Khan & Zawar Hussain, 2017. "A new estimator of finite population mean based on the dual use of the auxiliary information," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(9), pages 4425-4436, May.
    2. Shakeel Ahmed & Javid Shabbir & Sat Gupta, 2017. "Use of scrambled response model in estimating the finite population mean in presence of non response when coefficient of variation is known," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(17), pages 8435-8449, September.
    3. Mazhar Yaqub & Javid Shabbir, 2020. "Estimation of population distribution function involving measurement error in the presence of non response," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(10), pages 2540-2559, May.
    4. Siraj Muneer & Javid Shabbir & Alamgir Khalil, 2017. "Estimation of finite population mean in simple random sampling and stratified random sampling using two auxiliary variables," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(5), pages 2181-2192, March.
    5. Sardar Hussain & Sohaib Ahmad & Mariyam Saleem & Sohail Akhtar, 2020. "Finite population distribution function estimation with dual use of auxiliary information under simple and stratified random sampling," PLOS ONE, Public Library of Science, vol. 15(9), pages 1-30, September.
    6. Javid Shabbir & Sat Gupta, 2017. "Estimation of finite population mean in simple and stratified random sampling using two auxiliary variables," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(20), pages 10135-10148, October.
    7. Muñoz, J.F. & Arcos, A. & Álvarez, E. & Rueda, M., 2014. "New ratio and difference estimators of the finite population distribution function," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 102(C), pages 51-61.
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