A Refined Population Mean Estimator Using Median and Skewness: Applications to Breast Cancer and Brain Tumor Data
Bibliographic record
Abstract
Estimators are essential to sampling theory because they allow researchers and statisticians to calculate estimates of population parameters from observed data. In every survey activity, the experimenter aims to use methods that will improve the precision of population parameter estimations throughout both the design and estimation phases. When auxiliary data is used in the estimating, design, or both processes, these estimated precisions can be attained. By linearly merging the central value of the data under consideration with the skewness coefficient provided by Karl Pearson, this study created a new, improved predictor for calculating the average of a population. Estimators are crucial to sampling theory because of their capacity to produce estimates of population parameters from observed data. In this work, a novel modified ratio-type estimator was constructed by linearly merging Karl-Pearson's coefficient of skewness with the median value. Simple random sampling (SRS) was the technique employed in this present study. We conduct a numerical analysis from the standpoint of real estate. Additionally, we do some real data analysis on two distinct cancers: the brain tumor dataset and the breast cancer dataset. The results of the simulation study, real data application in the medical field, and numerical investigation show that the suggested estimator achieves lower error when the median value and Karl Pearson's coefficient of skewness are combined. Furthermore, compared to the other estimators under consideration, the one proposed in this study achieves better precision.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.012 | 0.040 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".