A Bivariate Extension of Type-II Generalized Crack Distribution for Modeling Heavy-Tailed Losses
Bibliographic record
Abstract
As an extension of the (univariate) Birnbaum–Saunders distribution, the Type-II generalized crack (GCR2) distribution, built on an appropriate base density, provides a sufficient level of flexibility to fit various distributional shapes, including heavy-tailed ones. In this paper, we develop a bivariate extension of the Type-II generalized crack distribution and study its dependency structure. For practical applications, three specific distributions, GCR2-Generalized Gaussian, GCR2-Student’s t, and GCR2-Logistic, are considered for marginals. The expectation-maximization algorithm is implemented to estimate the parameters in the bivariate GCR2 models. The model fitting results on a catastrophic loss dataset show that the bivariate GCR2 distribution based on the generalized Gaussian density fits the data significantly better than other alternative models, such as the bivariate lognormal distribution and some Archimedean copula models with lognormal or Pareto marginals.
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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 | 0.004 | 0.010 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 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".