Nearly unbiased estimators for the three‐parameter Weibull distribution with greater efficiency than the iterative likelihood method
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
The maximum likelihood estimation (MLE) method is the most commonly used method to estimate the parameters of the three-parameter Weibull distribution. However, it returns biased estimates. In this paper, we show how to calculate weights which cancel the biases contained in the MLE equations. The exact weights can be computed when the population parameters are known and the expected weights when they are not. Two of the three weights' expected values are dependent only on the sample size, whereas the third also depends on the population shape parameters. Monte Carlo simulations demonstrate the practicability of the weighted MLE method. When compared with the iterative MLE technique, the bias is reduced by a factor of 7 (irrespective of the sample size) and the variability of the parameter estimates is also reduced by a factor of 7 for very small sample sizes, but this gain disappears for large sample sizes.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| 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