The New Heavy‐Tailed Cosine‐Weibull Distribution: Properties, Simulation, Applications, and Regression Modeling
Why this work is in the frame
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Bibliographic record
Abstract
ABSTRACT The development of flexible probability distributions has become essential for accurately modelling real‐world data. In this study, we introduce a new three‐parameter lifetime model, the New Heavy‐Tailed Cosine‐Weibull (NHTCW) distribution, which extends the Cosine‐Weibull distribution using a heavy‐tailed framework. This extension enhances the model's capacity to capture skewness and tail behavior commonly observed in lifetime and survival data. We derive several statistical properties of the NHTCW distribution, including its ordinary and incomplete moments, quantile and generating functions, and order statistics. Maximum likelihood estimation (MLE) is used to estimate the model parameters, and a simulation study is conducted to evaluate the performance of the estimators in terms of accuracy and consistency. We propose a regression model based on the NHTCW distribution, making its first introduction in this context. The practical usefulness of the proposed distribution is demonstrated through three real‐data applications. Two data sets are related to COVID‐19 mortality rates in Italy and Canada, while the third is related to injury rate data. In all cases, the NHTCW model outperforms several existing distributions in terms of goodness‐of‐fit criteria, underscoring its flexibility and practical relevance.
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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 | 0.000 | 0.001 |
| 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