On<tex>$q$</tex>-Logistic and Related Models
Bibliographic record
Abstract
Numerous types of asymmetrical distributions such as the logistic, Weibull, gamma, and beta distributions have been used for modeling various random phenomena such as those encountered in data engineering, pattern recognition, and reliability assessment studies. Several generalizations of the logistic distribution, and certain related models, are proposed in this paper. The corresponding density functions involve an additional parameter, denoted by q, which allows for increased flexibility for modeling purposes; in fact, the larger this parameter is, the lower the mode of the resulting distribution will be. Generalizations of the type-1 and type-2 beta distributions are introduced, along with their logistic-type counterparts; the moments and cumulants of the latter are also derived. Other extensions are discussed including a q-analog of the generalized type-2 beta model, a q-extended generalized logistic distribution, and q-analogs of generalizations of the Dirichlet distribution. As is shown graphically, the proposed univariate distributions can generate a wide array of unimodal or symmetric bimodal curves.
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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 | 0.001 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.003 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.088 | 0.028 |
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".