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<p>Inflated data refers to datasets where certain values, such as zeros or specific points, appear significantly more often than expected under a given statistical model. This phenomenon is frequently observed across various fields, including economics, healthcare, and environmental studies. To address inflated data, l-inflated distributions are commonly used for modeling. The Poisson distribution is the most widely used approach for modeling inflated data; however, it has several limitations. An important alternative is the Telescopic family of distributions, which includes key discrete and some continuous distributions. This flexibility makes the Telescopic family a suitable choice for modeling both discrete and continuous inflated datasets. In addition to selecting an appropriate distribution, choosing an efficient sampling method is crucial. Ranked Set Sampling (RSS) is a powerful alternative to Simple Random Sampling (SRS), particularly in scenarios where ranking sample units within small sets is easier or more cost-effective than direct quantification. RSS has demonstrated broad applicability across numerous disciplines. In this study, we combine RSS with the Telescopic family of distributions to model inflated data. We evaluate the performance of RSS-based methods in comparison to their SRS-based counterparts using Monte Carlo simulations. Our results indicate that the RSS-based procedure consistently outperforms the SRS-based approach across various sample sizes, set sizes, and ranking quality levels. Finally, we apply our proposed methodology to real dataset, demonstrating its effectiveness in modeling advanced lung cancer datasets from the North Central Cancer Treatment Group.</p>

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l-inflated telescopic modeling using ranked set sampling with application to lung cancer data

  • 期刊论文

  • 发表日期：

    2026年6月25日

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  • Hadi Saboori,
  • Ehsan Zamanzade,
  • Hani M. Samawi

摘要

Inflated data refers to datasets where certain values, such as zeros or specific points, appear significantly more often than expected under a given statistical model. This phenomenon is frequently observed across various fields, including economics, healthcare, and environmental studies. To address inflated data, l-inflated distributions are commonly used for modeling. The Poisson distribution is the most widely used approach for modeling inflated data; however, it has several limitations. An important alternative is the Telescopic family of distributions, which includes key discrete and some continuous distributions. This flexibility makes the Telescopic family a suitable choice for modeling both discrete and continuous inflated datasets. In addition to selecting an appropriate distribution, choosing an efficient sampling method is crucial. Ranked Set Sampling (RSS) is a powerful alternative to Simple Random Sampling (SRS), particularly in scenarios where ranking sample units within small sets is easier or more cost-effective than direct quantification. RSS has demonstrated broad applicability across numerous disciplines. In this study, we combine RSS with the Telescopic family of distributions to model inflated data. We evaluate the performance of RSS-based methods in comparison to their SRS-based counterparts using Monte Carlo simulations. Our results indicate that the RSS-based procedure consistently outperforms the SRS-based approach across various sample sizes, set sizes, and ranking quality levels. Finally, we apply our proposed methodology to real dataset, demonstrating its effectiveness in modeling advanced lung cancer datasets from the North Central Cancer Treatment Group.