Delta diagram based test for the Halphen (A and B) and the Gamma distributions
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
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.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.013 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 it