Models of Insurance Claim Counts with Time Dependence Based on Generalization of Poisson and Negative Binomial Distributions
Bibliographic record
Abstract
Longitudinal data (or panel data) consist of repeated observations of individual units that are observed over time. Each individual insured is assumed to be independent but correlation between contracts of the same individual is permitted. This paper presents an exhaustive overview of models for panel data that consist of generalizations of count distributions where the dependence between contracts of the same insureds can be modeled with Bayesian and frequentist models, based on generalization of Poisson and negative binomial distributions. This paper introduces some of those models to actuarial science and compares the fitting with specification tests for nested and non-nested models. It also shows why some intuitive models (past experience as regressors, multivariate distributions, or copula models) involving time dependence cannot be used to model the number of reported claims. We conclude that the random effects models have a better fit than the other models examined here because the fitting is improved and it allows for more flexibility in computing the next year's premium.
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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 | 0.015 | 0.046 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.003 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.005 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.004 | 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".