Probability Models and Some Mathematical Techniques on Parameter Estimation for Daily Rainfall Extremes: Application to Daily Rainfall in Southern Thailand
Bibliographic record
Abstract
Abstract This study aims to identify the optimal distribution for modeling extreme events based on annual maximum series data from meteorological stations in Southern Thailand. We explored three types of two-parameter Generalized Extreme Value (GEV) distributions—Weibull, Fréchet, and Gumbel—and compared their fit to the observed data using GEV. The fitting process involved estimating model parameters, for which we employed two mathematical techniques: least square estimation and maximum likelihood estimation. Our findings revealed that, when fitting GEV distribution with numerical estimation for the shape parameter, the Gumbel distribution, characterized by a light-tail, is the most suitable for nearly all stations. However, when considering the two-parameter case for the three distribution types, the Fréchet distribution, known for its heavy-tail, emerges as the best fit for many stations, exhibiting the lowest ratio mean square error.
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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 | 0.005 | 0.021 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| 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".