On Selection of Probability Distributions for Representing Annual Extreme Rainfall Series
Bibliographic record
Abstract
This paper presents an assessment procedure for evaluating systematically the performance of various probability models in order to identify the most suitable distribution that could provide accurate extreme rainfall estimates. More specifically, nine popular probability distributions, Beta-K, Beta-P, Generalized Extreme Value (GEV), Generalized Normal (GNO), Generalized Pareto, Gumbel, Log-Pearson Type III, Pearson Type III, and Wakeby, were examined and compared for their descriptive and predictive abilities in the estimation of annual maximum precipitations. The suggested procedure was applied to 5-minute and 1-hour annual maximum precipitation data from a network of 20 raingages located in the southern Quebec region in Canada. The methods of maximum likelihood and L-moments were used to estimate the parameters of these distributions. Results based on numerical and graphical goodness-of-fit criteria have indicated that the Wakeby, GEV, and GNO models were the best models for describing the distribution of annual maximum precipitations in the southern Quebec region in Canada. Furthermore, it was found that no single distribution ranked best at every station for both rainfall durations. Additional bootstrap method was performed to evaluate the model ability at predicting extreme right-tail behaviour. The results are similar to the outcome of the goodness-of-fit tests. The GEV distribution, however, was preferred to the Wakeby and GNO because it requires a simpler parameter estimation method and it was based on a more solid theoretical basis for representing the distribution of extreme random variables. Therefore, among the nine candidate distributions considered, the GEV could be recommended as the most suitable model for describing the distribution of annual maximum precipitations in southern Quebec.
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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 | 0.020 | 0.079 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.005 | 0.003 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".