BEYOND THE PEARSON CORRELATION: HEAVY-TAILED RISKS, WEIGHTED GINI CORRELATIONS, AND A GINI-TYPE WEIGHTED INSURANCE PRICING MODEL
Bibliographic record
Abstract
Abstract Gini-type correlation coefficients have become increasingly important in a variety of research areas, including economics, insurance and finance, where modelling with heavy-tailed distributions is of pivotal importance. In such situations, naturally, the classical Pearson correlation coefficient is of little use. On the other hand, it has been observed that when light-tailed situations are of interest, and hence when both the Gini-type and Pearson correlation coefficients are well defined and finite, these coefficients are related and sometimes even coincide. In general, understanding how these correlation coefficients are related has been an illusive task. In this paper, we put forward arguments that establish such a connection via certain regression-type equations. This, in turn, allows us to introduce a Gini-type weighted insurance pricing model that works in heavy-tailed situations and thus provides a natural alternative to the classical capital asset pricing model. We illustrate our theoretical considerations using several bivariate distributions, such as elliptical and those with heavy-tailed Pareto margins.
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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 | 0.015 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.004 | 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 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".