Combining reliability functions of a Weibull distribution
Bibliographic record
Abstract
In this article, a large sample pooling procedure is considered for the reliability function of a Weibull distribution. Asymptotic properties of shrinkage estimation procedures based on the preliminary test are developed. It is shown that the proposed estimator has substantially smaller asymptoticmean squared error (AMSE) than the usual maximumlikelihood (ML) estimator inmost of the parameter space. Analytic AMSE expressions of the proposed estimators are obtained and the dominance picture of the estimators is presented by comparing them. It is shown that the suggested estimators yield a wider dominance range over theML estimator than the usual pretest estimator and give a meaningful size of the pretest. To appraise the small sample performance of the estimators, detailed Monte-Carlo simulation studies are also carried out.
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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 | 0.025 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.004 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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".