Univariate and multivariate mixtures of exponential distributions, with applications in risk modeling
Bibliographic record
Abstract
Abstract Mixed exponential distributions are frequently used in actuarial risk modeling. Distributions obtained through mixtures allow greater flexibility in the modeling of nonlife insurance loss amounts. Several research works have studied mixed exponential distributions in univariate and multivariate settings. The present article highlights the usefulness of such distributions and lays the story of the mixing technique behind them. It also explains the underlying link between all these works. We study in detail three univariate and multivariate mixed exponential distributions defined with a discrete mixing random variable (rv). For each of these three univariate (multivariate) mixed exponential distributions and using an appropriate scaling, we identify the continuous mixing rv to which converges in distribution the discrete mixing rv and the corresponding univariate (multivariate) mixed exponential distribution. In a multivariate setting, we show that these three choices of discrete mixing distributions lead us to known Archimedean copulas constructed with continuous mixing rvs. Applications in actuarial science of these distributions are presented throughout the article highlighting their many uses and useful properties.
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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 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.003 | 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".