A Novel Family of CDF Estimators Under PPS Sampling: Computational, Theoretical, and Applied Perspectives
Accurate estimation of population distribution characteristics is a fundamental task in survey sampling and statistical inference. This paper introduces a new family of estimators for the cumulative distribution function (CDF) under probability proportional to size (PPS) sampling, incorporating auxi...
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| Formato: | Artículo |
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2025
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| author | Shah, Salman Mahmoudi, Eisa Iftikhar, Hasnain Rodrigues, Paulo Canas Gonzales Medina, Ronny Ivan López Gonzales, Javier Linkolk |
| author_browse | Gonzales Medina, Ronny Ivan Iftikhar, Hasnain López Gonzales, Javier Linkolk Mahmoudi, Eisa Rodrigues, Paulo Canas Shah, Salman |
| author_facet | Shah, Salman Mahmoudi, Eisa Iftikhar, Hasnain Rodrigues, Paulo Canas Gonzales Medina, Ronny Ivan López Gonzales, Javier Linkolk |
| author_sort | Shah, Salman |
| collection | Producción científica |
| description | Accurate estimation of population distribution characteristics is a fundamental task in survey sampling and statistical inference. This paper introduces a new family of estimators for the cumulative distribution function (CDF) under probability proportional to size (PPS) sampling, incorporating auxiliary information to enhance efficiency. The proposed approach employs dual auxiliary variables in the estimation phase, while the sampling design relies on a single auxiliary variable. Theoretical properties, including bias and mean squared error (MSE), are rigorously derived to establish the efficiency of the new class. An extensive empirical evaluation using three distinct populations—fisheries data, wine chemistry data, and demographic records—demonstrates the superiority of the proposed estimators. In terms of accuracy, the best-performing proposed estimator achieves an MSE of 0.0012, compared to 0.0127 for the widely used GK estimator. Percentage relative efficiency (PRE) values further underscore these improvements, with gains ranging from 123% to over 328% across the three populations. Graphical comparisons confirm these trends, illustrating that the proposed estimators consistently dominate conventional approaches. Overall, the findings highlight both the theoretical soundness and practical utility of the proposed family, offering robust and computationally efficient improvements for CDF estimation in complex survey designs. |
| format | Article |
| id | oai:cris.upeu.edu.pe:20.500.15037/398 |
| institution | UPeU |
| language | English |
| publishDate | 2025 |
| publishDateRange | 2025 |
| publishDateSort | 2025 |
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| spelling | oai:cris.upeu.edu.pe:20.500.15037/3982026-10-30T16:14:36ZA Novel Family of CDF Estimators Under PPS Sampling: Computational, Theoretical, and Applied PerspectivesShah, SalmanMahmoudi, EisaIftikhar, HasnainRodrigues, Paulo CanasGonzales Medina, Ronny IvanLópez Gonzales, Javier Linkolkprobability proportional to size (PPS) samplingcumulative distribution function (CDF) estimationauxiliary informationdual auxiliary variablesefficiency analysissimulation studyAccurate estimation of population distribution characteristics is a fundamental task in survey sampling and statistical inference. This paper introduces a new family of estimators for the cumulative distribution function (CDF) under probability proportional to size (PPS) sampling, incorporating auxiliary information to enhance efficiency. The proposed approach employs dual auxiliary variables in the estimation phase, while the sampling design relies on a single auxiliary variable. Theoretical properties, including bias and mean squared error (MSE), are rigorously derived to establish the efficiency of the new class. An extensive empirical evaluation using three distinct populations—fisheries data, wine chemistry data, and demographic records—demonstrates the superiority of the proposed estimators. In terms of accuracy, the best-performing proposed estimator achieves an MSE of 0.0012, compared to 0.0127 for the widely used GK estimator. Percentage relative efficiency (PRE) values further underscore these improvements, with gains ranging from 123% to over 328% across the three populations. Graphical comparisons confirm these trends, illustrating that the proposed estimators consistently dominate conventional approaches. Overall, the findings highlight both the theoretical soundness and practical utility of the proposed family, offering robust and computationally efficient improvements for CDF estimation in complex survey designs.Articlehttps://doi.org/10.3390/axioms1411079610.3390/axioms14110796https://hdl.handle.net/20.500.15037/398W4415683822enAxioms2075-16802025-10-292026-06-13T08:12:41Z2026-06-13T08:12:41Z |
| spellingShingle | probability proportional to size (PPS) sampling cumulative distribution function (CDF) estimation auxiliary information dual auxiliary variables efficiency analysis simulation study Shah, Salman Mahmoudi, Eisa Iftikhar, Hasnain Rodrigues, Paulo Canas Gonzales Medina, Ronny Ivan López Gonzales, Javier Linkolk A Novel Family of CDF Estimators Under PPS Sampling: Computational, Theoretical, and Applied Perspectives |
| title | A Novel Family of CDF Estimators Under PPS Sampling: Computational, Theoretical, and Applied Perspectives |
| title_full | A Novel Family of CDF Estimators Under PPS Sampling: Computational, Theoretical, and Applied Perspectives |
| title_fullStr | A Novel Family of CDF Estimators Under PPS Sampling: Computational, Theoretical, and Applied Perspectives |
| title_full_unstemmed | A Novel Family of CDF Estimators Under PPS Sampling: Computational, Theoretical, and Applied Perspectives |
| title_short | A Novel Family of CDF Estimators Under PPS Sampling: Computational, Theoretical, and Applied Perspectives |
| title_sort | novel family of cdf estimators under pps sampling computational theoretical and applied perspectives |
| topic | probability proportional to size (PPS) sampling cumulative distribution function (CDF) estimation auxiliary information dual auxiliary variables efficiency analysis simulation study |
| topic_facet | probability proportional to size (PPS) sampling cumulative distribution function (CDF) estimation auxiliary information dual auxiliary variables efficiency analysis simulation study |
| url | https://doi.org/10.3390/axioms14110796 https://hdl.handle.net/20.500.15037/398 |
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