Delta diagram based test for the Halphen (A and B) and the Gamma distributions
Bibliographic record
Abstract
The most used statistical distributions to fit extreme value data in hydrology, can be regrouped in three classes: class C of regularly varying distributions and class D of sub exponential distributions, depending on their tail behaviour. The Halphen distributions (Halphen type A (HA) and Halphen type B (HB)) have both the Gamma (G2) distribution as limiting case and all these three distributions belong to the class D and can be displayed in the (Delta1 = ln(A/G); Delta2 = ln(G/H)) moment ratio diagram based on Geometric (G), Arithmetic (A) and Harmonic (H) means. In this study, a statistical test for discriminating between HA, HB and the Gamma distribution is developed. The methodology is based on Monte Carlo simulation for (1) the determination of the confidence regions around the Gamma curve for each fixed couple (Delta1 , Delta2) and (2) the study of the power of the proposed test for both alternatives HA and HB distributions and comparison with the Likelihood Ratio Test (LRT). Results showed that the test is powerful especially for high values of skewness and is far better than the LRT. This test will be included, shortly, in Decision Support System (DSS) of the HYFRAN-PLUS software.
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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 | 0.010 | 0.065 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.004 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.008 | 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".