A new Maxwell-Log logistic distribution and its applications for mortality rate data
Bibliographic record
Abstract
In this research, we extended the Log-Logistic distribution by incorporating it into the Maxwell generalized class, resulting in the Maxwell-Log Logistic (Max-LL ) distribution. The probability density function and cumulative distribution function of the proposed distribution have been defined. The proposed distribution’s density shapes can be left or right-skewed and symmetric. The failure function of this distribution might be increasing, decreasing, or inverted bathtub forms. We discussed some essential properties of the Max-LL distribution, including moments, moment generating function, probability weighted moments, stress-strength, and order statistics. The efficiency of the model parameters has been evaluated through a simulation study utilizing a quantile function. To assess the proposed distribution’s adaptability, we applied it to two lifetime datasets: global COVID-19 mortality rates (for nations with more than 100,000 cases) and Canadian COVID-19 mortality rates. The Maxwell-Log Logistic distribution outperformed other distributions on both datasets, as evidenced by several accuracy measures. This shows that the proposed distribution is the best fit for COVID-19 mortality rate data in Canada and around the world.
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How this classification was reachedexpand
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 | 0.003 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".