Bibliographic record
Abstract
Probability distributions with identical shape factor asymptotic limit formulas are defined as asymptotic equivalent distributions.The GB1, GB2, and Generalized Gamma distributions are examples of asymptotic equivalent distributions, which have similar fitting capabilities to data distribution with comparable parameters values.These example families are also asymptotic equivalent to Kumaraswamy, Weibull, Beta, ExpGamma, Normal, and LogNormal distributions at various parameters boundaries.The asymptotic analysis that motivated the asymptotic equivalent distributions definition is further generalized to contour analysis, with contours not necessarily parallel to the axis.Detailed contour analysis is conducted for GB1 and GB2 distributions for various contours of interest.Methods combing induction and symbolic deduction are crafted to resolve the dilemma over conflicting symbolic asymptotic limit results.From contour analysis build on graphical and analytical reasoning, we find that the upper bound of the GB2 distribution family, having the maximum shape factor for given skewness, is attained by the Double Pareto 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 | 0.004 | 0.034 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.004 | 0.003 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.004 |
| Insufficient payload (model declined to judge) | 0.008 | 0.003 |
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".