The Bayes Premium in an Aggregate Loss Poisson-Lindley Model with Structure Function STSP
Bibliographic record
Abstract
Many premium calculating problems in actuarial science consider the number of claims, denoted as K, as the variable risk. Traditionally, this random variable is modelled by the Poisson distribution. However, it is well known that automobile insurance portfolios are characterized by zero-inflation (high percentage of zero values in the sample) and overdispersion (the variance is greater than the mean), and the Poisson distribution does not properly reflect the last phenomenon. In this paper we determine the Bayes premium considering that K follows a Poisson-Lindley distribution, with parameter $\theta_{1}$ in $[0,1]$, which is a potential alternative to describe these situations. As the structure function for $\theta_{1}$ we elicit the standardized two-sided power distribution, which is a reasonable alternative to the usual beta distribution. In addition, an aggregate loss model is considered with primary distribution given by the Poisson-Lindley distribution. A Bayesian analysis is developed to obtain the Bayes premium. The conclusion is that the STSP is not an adequate alternative in the problem in question because it is more informative and less dispersed than the Beta distribution.
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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 | 0.009 | 0.019 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.003 | 0.003 |
| Insufficient payload (model declined to judge) | 0.005 | 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".