Modeling under or over-dispersed binomial count data by using extended Altham distribution families
Bibliographic record
Abstract
While aiming particularly at handling under-dispersion, we explore a type of models constructed conservatively using the minimum information of first two moments for the fitting of binomial count data, which could have under, equal or over-dispersion. The extended Altham distribution (EAD) families were presented in this study. The extended Altham families are very close to the binomial distribution under equal dispersion setting, implying that they are alternative models of the binomial distribution. The feature that extended Altham families can reach the full range of dispersion outperforms some commonly used models such as extended beta-binomial and quasi-binomial which have restricted ranges of dispersion. Moreover, the extended Altham family can have double peaks at two boundaries, indicating they are feasible for fitting the double tail inflation phenomenon. This study illustrated the modeling using extended Altham families for both under-dispersed and over-dispersed binomial data resulted from disease cases within the same family.
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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 | 0.011 | 0.038 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| 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".