Comparison of two fitting methods for the log‐logistic distribution
Bibliographic record
Abstract
We investigate generalized probability weighted moments (GPWM) and maximum likelihood (ML) fitting methods in the two‐parameter log‐logistic (LL) model. Parameter and quantiles estimators are computed along with their asymptotic variances and covariances. A comparison of these methods is done by simulation. It is concluded that for estimating β, GPWM can provide better results than the ML method. However, for estimating quantiles, GPWM provides better results only for very small sample sizes, especially when the distribution is quite asymmetrical. Although presently, LL is not one of the distributions frequently used in hydrology, we agree with some authors that it merits wider use in hydrological practice. For a clearer idea on the merits of LL, we compare it with three other distributions for fitting flood data from 114 hydrometric stations in Canada. The results support our view regarding the good fitting potential of the LL distribution to extreme hydrologic data.
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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 | 0.006 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 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) | 0.001 | 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 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".