A flexible extended generalized Pareto distribution for tail estimation
Why this work is in the frame
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Bibliographic record
Abstract
Abstract For both financial and environmental applications, tail distributions often correspond to extreme risks and an accurate modeling is mandatory. The peaks‐over‐threshold model is a classic way to model the exceedances over a high threshold with the generalized Pareto distribution. However, for some applications, the choice of a high threshold is challenging and the asymptotic conditions for using this model are not always satisfied. The class of extended generalized Pareto models can be used in this case. However, the existing extended model have either infinite or null density at the threshold, which is not consistent with tail modeling. In the present article, we propose new extensions of the generalized Pareto distribution for which the density at the threshold is positive and finite. The proposed extensions provide better estimate of the upper tail index for low thresholds than existing models. They are also appropriate for high thresholds because in that case, the extended models simplify to the generalize Pareto model. The performance and flexibility of the models are illustrated with the modeling of temperature exceeding a low threshold and non‐zero precipitations recorded in Montreal. For non‐zero precipitation, the very low threshold of 0 is used.
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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 | 0.000 |
| 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 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.006 | 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