Discriminating between the Lognormal and the Log-Logistic Distributions for Hydrological Frequency Analysis
Why this work is in the frame
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Bibliographic record
Abstract
Discriminating between competitive statistical models is an important problem in hydrological frequency analysis. The present study deals with discrimination between the two-parameter lognormal (LN2) and the two-parameter log-logistic (LLOG2) distributions, or, equivalently, between the normal (N) and the logistic (LOG) distributions. Previous work using the likelihood ratio (LR) statistic suggested that discrimination between these distributions is difficult, and that criteria other than LR need to be studied in hope of finding criteria with better discriminating power. In the present study, several criteria other than LR are considered, and their ability to discriminate between the LN2 and LLOG2 distributions is assessed using Monte Carlo simulation. The results confirm previous findings that discrimination between the two distributions is difficult with small samples, but a criterion based on the Shapiro-Wilk statistic appears to be the most appropriate for sample sizes typically encountered in hydrology. Two hydrological examples are presented to illustrate how obtained results can be implemented in practice.
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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 | 0.001 | 0.000 |
| 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