An Extension of the Gompertz Distribution for Modeling COVID-19 Mortality Dynamics
Bibliographic record
Abstract
The Gompertz distribution is widely used in medical and reliability studies, particularly for modeling mortality rates and failure data. However, it has limitations in capturing complex data behaviors, such as heavy tails and varying hazard rate shapes. This paper introduces the Odd Beta Prime-Gompertz (OBP-Gompertz) distribution, a four-parameter extension of the traditional Gompertz model. The OBP-Gompertz distribution offers flexibility in modeling various shapes of probability density functions, including right-skewed, left-skewed, heavy-tailed, light-tailed, and unimodal distributions. Its hazard function can accommodate multiple forms, such as increasing, decreasing, bathtub-shaped, and inverted bathtub-shaped curves, making it well-suited for mortality rate data. The paper investigates key statistical properties, including moments, moment generating function, quantile function, Rényi and Tsallis entropy measures. Parameters are estimated using maximum likelihood estimation, and the model's robustness is assessed through Monte Carlo simulations. The OBP-Gompertz model is applied to three real-world COVID-19 mortality datasets from China, the Netherlands, and Nepal. The results demonstrate that the OBP-Gompertz model provides superior fits compared to the traditional Gompertz and other models. This work highlights the OBP-Gompertz distribution as a valuable tool for survival analysis, reliability studies, and epidemiological research.
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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 | 0.017 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.003 | 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 | 0.003 |
| Insufficient payload (model declined to judge) | 0.004 | 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".