Exact Inference for Laplace Quantile, Reliability, and Cumulative Hazard Functions Based on Type-II Censored Data
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Bibliographic record
Abstract
In this paper, we first present explicit expressions for the maximum likelihood estimates (MLEs) of the location, and scale parameters of the Laplace distribution based on a Type-II right censored sample under different cases. Then, after giving the exact density functions of the MLEs, and the expectations, we derive the exact density of the MLE of the quantile, and utilize it to develop exact confidence intervals for the population quantile. We also briefly discuss the MLEs of reliability and cumulative hazard functions, and how to develop exact confidence intervals for these functions. These results can also be extended to any linear estimators. Finally, we present two examples to illustrate the inferential methods developed here.
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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 | 0.001 | 0.003 |
| 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