Higher order inference for stress–strength reliability with independent Burr-type <i>X</i> distributions
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Bibliographic record
Abstract
In this paper, a small-sample asymptotic method is proposed for higher order inference in the stress–strength reliability model, R=P(Y<X), where X and Y are distributed independently as Burr-type X distributions. In a departure from the current literature, we allow the scale parameters of the two distributions to differ, and the likelihood-based third-order inference procedure is applied to obtain inference for R. The difficulty of the implementation of the method is in obtaining the the constrained maximum likelihood estimates (MLE). A penalized likelihood method is proposed to handle the numerical complications of maximizing the constrained likelihood model. The proposed procedures are illustrated using a sample of carbon fibre strength data. Our results from simulation studies comparing the coverage probabilities of the proposed small-sample asymptotic method with some existing large-sample asymptotic methods show that the proposed method is very accurate even when the sample sizes are small.
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 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