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<p>This study derives the likelihood function for Ranked Set Sampling (RanSS) and Neoteric Ranked Set Sampling (NeRanSS) with Censoring Type-II. It applies to the estimation of Unit Gompertz Distribution (UGD) parameters, demonstrating enhanced estimation accuracy and efficiency. The study compares the efficiency of RanSS and NeRanSS against traditional Simple Random Sampling (SRS) based on Censoring Type-II for estimating UGD parameters. Choosing an RSS scheme is beneficial when ranking elements is less costly than measuring them, when precision is essential, or when practical constraints limit sample size. The UGD, constructed through a transformation of the Gompertz distribution, is widely utilized in survival analysis and reliability studies. A Monte Carlo simulation evaluates the performance of these sampling methods under Censoring Type-II, focusing on Mean Squared Error (MSE), Bias, and efficiency. Results show that NeRanSS consistently outperforms RanSS and SRS, yielding the lowest MSE and highest efficiency, particularly for larger sample sizes, as confirmed by efficiency metrics. While NeRanSS generally provides competitive bias, it does not always produce the lowest bias across all parameter settings. These findings position NeRanSS as a superior method for UGD parameter estimation.</p>

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Comparative Study for Parametric Estimation Based on Ranked Set Sampling through Censoring Cases

  • 期刊论文

  • 发表日期：

    2025年7月29日

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  • Hiba Z. Muhammed,
  • Mostafa Shaaban

摘要

This study derives the likelihood function for Ranked Set Sampling (RanSS) and Neoteric Ranked Set Sampling (NeRanSS) with Censoring Type-II. It applies to the estimation of Unit Gompertz Distribution (UGD) parameters, demonstrating enhanced estimation accuracy and efficiency. The study compares the efficiency of RanSS and NeRanSS against traditional Simple Random Sampling (SRS) based on Censoring Type-II for estimating UGD parameters. Choosing an RSS scheme is beneficial when ranking elements is less costly than measuring them, when precision is essential, or when practical constraints limit sample size. The UGD, constructed through a transformation of the Gompertz distribution, is widely utilized in survival analysis and reliability studies. A Monte Carlo simulation evaluates the performance of these sampling methods under Censoring Type-II, focusing on Mean Squared Error (MSE), Bias, and efficiency. Results show that NeRanSS consistently outperforms RanSS and SRS, yielding the lowest MSE and highest efficiency, particularly for larger sample sizes, as confirmed by efficiency metrics. While NeRanSS generally provides competitive bias, it does not always produce the lowest bias across all parameter settings. These findings position NeRanSS as a superior method for UGD parameter estimation.