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Exploring mixture estimators in stratified random sampling.

Kanwal Iqbal1,2, Syed Muhammad Muslim Raza1,3, Tahir Mahmood4

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This study introduces a new mixture estimator for population mean estimation using auxiliary variables under stratified sampling. The proposed method enhances precision across various distributions and sample sizes, outperforming existing estimators.

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Area of Science:

  • Statistics
  • Survey Methodology
  • Data Science

Background:

  • Modern sensor technology enables vast data generation, necessitating efficient statistical methods.
  • Auxiliary variables (quantitative and qualitative) are often recorded alongside study variables for cost-effectiveness.
  • Mixture estimators are valuable for leveraging auxiliary information to estimate population means.

Purpose of the Study:

  • To propose a generalized family of mixture estimators for stratified sampling.
  • To enhance the precision of population mean estimation using auxiliary variables.
  • To analyze the behavior of the proposed estimators across different sample sizes and distributions.

Main Methods:

  • Development of generalized mixture estimators under stratified sampling.
  • Investigation of estimator efficiency for symmetrical and asymmetrical distributions.
  • Analysis of estimator convergence to the Normal distribution with varying sample sizes.

Main Results:

  • The proposed generalized mixture estimator demonstrates higher precision compared to existing methods.
  • The estimator's performance was validated across Normal, Uniform, Weibull, and Gamma distributions.
  • The estimator follows Cauchy distribution for sample sizes < 35, converging to normality thereafter.

Conclusions:

  • The proposed generalized mixture estimators offer a significant improvement in estimating population means.
  • The findings are supported by real-world applications in health and finance sectors.
  • The study highlights the importance of considering sample size and data distribution for estimator selection.