Burr III Scaled Inverse Odds Ratio‐Weibull Distribution for Modeling Asymmetric Medical and Engineering Data
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
ABSTRACT This article introduces the novel five‐parameter Burr III Scaled Inverse Odds Ratio‐Weibull (B‐SIOR‐W) distribution, a flexible extension of the classical two‐parameter Weibull model, specifically engineered to model asymmetric data prevalent in medical and engineering domains. We present a comprehensive analysis of its statistical properties, including moments, the moment generating function, entropy, and order statistics, with parameters estimated using Maximum Likelihood Estimation (MLE), confirmed for efficiency and consistency via a robust simulation study. The B‐SIOR‐W distribution's competitive advantage is conclusively demonstrated against the parent and competing models using two diverse real‐world datasets: COVID‐19 mortality rates (Canada) and active repair times for an airborne communication transceiver, which constitutes the primary findings. This enhanced modeling precision is highly significant in domains like public health epidemiology and reliability engineering, where accurate risk assessment and prediction are critical. Furthermore, we illustrate its practical utility by designing a Group Acceptance Sampling Plan (GASP), leveraging the estimates from the COVID‐19 data to provide actionable insights for product quality specification and control.
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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 | 0.009 |
| 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