Statistical Tools for Choices between Probability Distributions for Hydrological Frequency Modelling
Bibliographic record
Abstract
Two-parameter probability distributions are among those frequently employed in hydrological frequency modeling, especially in the peaks-over-threshold approach to analysing hydrological extremes. When the practitioner fits several candidate models to a data set, selection of the final fitting model often reduces to having to pick, or “discriminate,” between one specific pair of competitive models. We will review some widely used discrimination statistics (DS) in terms of their ability for correct selection between pairs of competitive 2-parameter models. We will also attempt to classify model pairs according to the difficulty to discriminate between them. Research has shown three DS to be among those most capable of correctly selecting between pairs of 2-parameter models. These DS are: (1) the ratio of maximized likelihood statistic—RML (closely associated with the Akaike Information Criterion—AIC and the Bayesian Information Criterion—BIC), (2) the Anderson-Darling (AD) goodness-of-fit (GoF) statistic, and (3) a (relatively new) DS derived from the Shapiro-Wilk GoF statistic, which we will denote by “TN.SW.” Research has shown the TN.SW DS to be advantageous when applied to samples of size typically encountered in hydrology. A hydrological example will show the use of this DS in practice.
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How this classification was reachedexpand
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 | 0.000 | 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 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 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 teacher head, 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".