A new Cosine-Weibull model: Distributional properties with applications to basketball and medical sectors
Bibliographic record
Abstract
The two-parameter classical Weibull distribution is commonly implemented to cater for the product’s reliability, model the failure rates, analyze lifetime phenomena, etc. In this work, we study a novel version of the Weibull model for analyzing real-life events in the sports and medical sectors. The newly derived version of the Weibull model, namely, a new cosine-Weibull (NC-Weibull) distribution. The importance of this research is that it suggests a novel version of the Weibull model without adding any additional parameters. Different distributional properties of the NC-Weibull distribution are obtained. The maximum likelihood approach is implemented to estimate the parameters of the NC-Weibull distribution. Finally, three applications are analyzed to prove the superiority of the NC-Weibull distribution over some other existing probability models considered in this study. The first and second applications, respectively, show the mortality rates of COVID-19 patients in Italy and Canada. Whereas, the third data set represents the injury rates of the basketball players collected during the 2008–2009 and 2018–2019 national basketball association seasons. Based on four selection criteria, it is observed that the NC-Weibull distribution may be a more suitable model for considering the sports and healthcare data sets.
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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 | 0.005 | 0.014 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.003 | 0.001 |
| 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".