Burr III Scaled Inverse Odds Ratio‐Weibull Distribution for Modeling Asymmetric Medical and Engineering Data
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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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.013 | 0.041 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".