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A Simulation Study on Some Confidence Intervals for Estimating the Population Mean Under Asymmetric and Symmetric Distribution Conditions |
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PP: 123-144 |
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Author(s) |
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H M Nayem,
B. M. Golam Kibria,
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Abstract |
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| This study presents a comprehensive review and comparison of several methods for estimating the population mean using confidence intervals. The analysis considers both symmetric and asymmetric distributions while accounting for outliers. It evaluates 23 different estimators within classical and modified-t approaches by conducting a simulation study, covering symmetric and skewed distributions. The simulation results reveal that the proposed Q1-t, Q3-t, Q1Q3-t, Wizard-t, and Wizard-t from the median are particularly robust for moderate sample sizes and asymmetric populations. Conversely, Student-t emerges as the top performer for small sample sizes for symmetric distribution. Additionally, Chen-t, Median-t, T1, AADM-t, and Median-t estimators show promise for skewed distributions. Findings indicate that the ordinary t estimator performs optimally for symmetric distributions and small sample sizes, exhibiting a superior coverage rate and minimum width compared to other estimators. For skewed distributions, the Median-t, AADM-t, Median T1, Chen-t, and YY-t statistics are proposed as effective options for mean estimation. Notably, for moderate sample sizes (>50), the newly proposed Wizard-t and Wizard-t from median methods consistently demonstrate higher coverage rates and smaller confidence interval widths, surpassing other test statistics. Real-life data analysis further supports these findings. This study contributes valuable insights for practitioners by offering a comprehensive overview of available estimators for estimating the population mean across various distributional scenarios.
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