Probability Models and Some Mathematical Techniques on Parameter Estimation for Daily Rainfall Extremes: Application to Daily Rainfall in Southern Thailand
Bibliographic record
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 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 | 0.002 | 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 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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".