On Heavy-tailed Crack Distribution for Loss Severity Modeling
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Bibliographic record
Abstract
Heavy-tailedness and right-skewness are two typical features of loss data resulting from catastrophic events such as storms or earthquakes. In this paper we study the tail properties of the generalized crack distribution which has recently been introduced as an extension of the Birnbaum-Saunders distribution and the three-parameter Gaussian crack distribution. The theoretical tail relationships between the auxiliary (or baseline) distribution and the resulting generalized crack distribution are studied relying on the classical theories of extreme values and regular variation. A few concrete examples of heavy-tailed crack distribution are constructed and used for model fitting exercises on both simulated and real catastrophic loss data sets. The fitting results show that the heavy-tailed crack distribution with an appropriate choice of baseline density function outperforms some other commonly used parametric models.
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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 | 0.001 | 0.002 |
| 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