Effective Estimation Methods Through Ranked Set Sampling for Mixture Model: Industrial and Survival Applications
Bibliographic record
Abstract
The sampling strategy has a considerable impact on the representativeness of the sampled data and can lead to incorrect estimates if not carefully chosen. An improved method over more conventional simple random sampling (SRS) is ranked set sampling (RSS). The RSS is more efficient, reducing the number of measurements needed for a desired level of precision, especially in challenging data collection scenarios. The Monsef distribution is a recent mixture lifetime model that has demonstrated effectiveness in modeling various real-world datasets. Several mathematical aspects of the Monsef distribution include quantiles, upper incomplete moments, lower incomplete moments, stochastic ordering, and extropy measures. This work investigates the use of RSS in conjunction with several traditional estimation techniques to estimate the parameters of the Monsef distribution. Fifteen different estimation procedures are investigated, including maximum product spacing, some minimum spacing distance methods, the Kolmogorov method, ordinary least squares, maximum likelihood, and weighted least squares. To assess the performance of the estimation techniques for a range of sample sizes under perfect ranking conditions and both sampling techniques, a simulation scenario is conducted. The partial and total ranks of numerous estimates are displayed to determine the best estimation approach. According to simulation results, the maximum likelihood and maximum product spacing approaches consistently outperform other methods in evaluating the estimated quality for both RSS and SRS. To demonstrate the feasibility of the different methods, three authentic datasets from various fields are examined.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".