The fallacy of large shape parameters when using the two-parameter weibull distribution
Why this work is in the frame
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Bibliographic record
Abstract
The Weibull distribution is used to characterize the parameters of survival data. However, the two-parameter version of the Weibull model does not include a shift parameter. As the first breakages are sometimes occurring far from 0, the shape of the 2-parameter Weibull distribution must be extreme to accommodate such data. Here we show that Weibull distributions with extreme shapes are degenerate distributions which do not contain information about shape anymore. Because of this, any 2- parameter Weibull distribution with large shape parameter can be mimicked by another large-shaped distribution. The argument is further illustrated with simulated results. We present simple solutions to detect and avoid such situations.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 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 it