Parameters Estimation for Wear-out Failure Period of Three-Parameter Weibull Distribution
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Bibliographic record
Abstract
The shape parameter estimation using the minimum-variance linear estimator with hyperparameter (MVLE-H) method is believed to be effective for a wear-out failure period in a small sample. In the process of the estimation, our method uses the hyperparameter and estimate shape parameters of the MVLE-H method. To obtain the optimal hyperparameter c, it takes a long time, even in the case of the small sample. The main purpose of this paper is to remove the restriction of small samples. We observed that if we set the shape parameters, for sample size n and c, we can use the regression equation to infer the optimal c from n. So we searched in five increments and complemented the hyperparameter for the remaining sample sizes with a linear regression line. We used Monte Carlo simulations (MCSs) to determine the optimal hyperparameter for various sample sizes and shape parameters of the MVLE-H method. Intrinsically, we showed that the MVLE-H method performs well by determining the hyperparameter. Further, we showed that the location and scale parameter estimations are improved using the shape parameter estimated by the MVLE-H method. We verified the validity of the MVLE-H method using MCSs and a numerical example.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 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