Discriminating between the Lognormal and the Log-Logistic Distributions for Hydrological Frequency Analysis
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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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 | 0.013 | 0.085 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".