Reflections on Some Methods Used to Fit Statistical Distributions to Hydrological Data
Bibliographic record
Abstract
Among the methods used to fit statistical distributions to extreme hydrological data are the methods of maximum likelihood (ML), of moments (MM), and of probability weighted moments (PWM), in addition to two classes of relatively recent methods, which are the methods of generalized moments (GM) and of generalized probability weighted moments (GPWM). We review some previously published results and share some recently obtained ones pertaining to the relative performance of these fitting methods. Particular attention is given to the capacity of these methods to estimate shape parameters of populations and distribution quantiles. Reflections are made on the effect of sample and population characteristics on the performance of the various fitting methods. The Pareto, log-logistic and Weibull distributions are used to aid in the discussion.
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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 | 0.037 | 0.104 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.004 | 0.005 |
| Science and technology studies | 0.001 | 0.010 |
| Scholarly communication | 0.005 | 0.010 |
| Open science | 0.004 | 0.003 |
| Research integrity | 0.004 | 0.018 |
| Insufficient payload (model declined to judge) | 0.004 | 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".