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Enhanced Estimation of the Population Mean Using Two Auxiliary Variables under Probability Proportional to Size Sampling

Author

Listed:
  • Sohaib Ahmad
  • Erum Zahid
  • Javid Shabbir
  • Muhammad Aamir
  • Ronald Onyango

Abstract

In some situations, the population of interest differs significantly in size, for example, in a medical study, the number of patients having a specific disease and the size of health units may vary. Similarly, in a survey related to the income of a household, the household may have a different number of siblings, and then in such situations, we use probability proportional to size sampling. In this article, we have proposed an improved class of estimators for the estimation of population mean on the basis of probability proportional to size (PPS) sampling, using two auxiliary variables. The mathematical expressions of the bias and mean square error (MSE) are derived up to the first order of approximation. Four real datasets and a simulation study are conducted to assess the efficiency of the improved class of estimators. It is found from the real datasets and a simulation study, that the proposed generalized class of estimators produced better results in terms of minimum MSE and higher PRE, as related to other considered estimators. An empirical study is given to support the theoretical results. The theoretical study also demonstrates that the proposed generalized class of estimators outperforms the existing estimators.

Suggested Citation

  • Sohaib Ahmad & Erum Zahid & Javid Shabbir & Muhammad Aamir & Ronald Onyango, 2023. "Enhanced Estimation of the Population Mean Using Two Auxiliary Variables under Probability Proportional to Size Sampling," Mathematical Problems in Engineering, John Wiley & Sons, vol. 2023(1).
    • Handle: RePEc:wly:jnlmpe:v:2023:y:2023:i:1:n:5564360
    DOI: 10.1155/2023/5564360
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    References listed on IDEAS

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    1. Garib Nath Singh & Mohd Khalid, 2015. "Exponential chain dual to ratio and regression type estimators of population mean in two-phase sampling," Statistica, Department of Statistics, University of Bologna, vol. 75(4), pages 379-389.
    2. Fariha Sohil & Muhammad Umair Sohail & Javid Shabbir, 2022. "Optimum second call imputation in PPS sampling," PLOS ONE, Public Library of Science, vol. 17(1), pages 1-17, January.
    3. Ina Trolle Andersen & Ute Hahn & Eva B. Vedel Jensen, 2015. "Optimal PPS Sampling with Vanishing Auxiliary Variables – with Applications in Microscopy," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(4), pages 1136-1148, December.
    4. Al-Omari, Amer Ibrahim, 2012. "Ratio estimation of the population mean using auxiliary information in simple random sampling and median ranked set sampling," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 1883-1890.
    5. Shashi Bhushan & Anoop Kumar & Ronald Onyango & Saurabh Singh & Alessandro Barbiero, 2022. "Some Improved Classes of Estimators in Stratified Sampling Using Bivariate Auxiliary Information," Journal of Probability and Statistics, Hindawi, vol. 2022, pages 1-23, August.
    6. Sohaib Ahmad & Sardar Hussain & Uzma Yasmeen & Muhammad Aamir & Javid Shabbir & M El-Morshedy & Afrah Al-Bossly & Zubair Ahmad, 2022. "A simulation study: Using dual ancillary variable to estimate population mean under stratified random sampling," PLOS ONE, Public Library of Science, vol. 17(11), pages 1-19, November.
    7. M. Mahdizadeh & Ehsan Zamanzade, 2020. "Estimation of a symmetric distribution function in multistage ranked set sampling," Statistical Papers, Springer, vol. 61(2), pages 851-867, April.
    8. Satish Kumar Agarwal & Mariam Al Mannai, 2009. "Linear combination of estimators in probability proportional to sizes sampling to estimate the population mean and its robustness to optimum value," Statistica, Department of Statistics, University of Bologna, vol. 69(1), pages 59-71.
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