Some Parameter Estimators in the Generalized Pareto Model and Their Inconsistency with Observed Data
Bibliographic record
Abstract
The generalized Pareto distribution (GPD) is widely used in the frequency modeling of hydrological extremes. Statistical methods used to fit this model to data include the methods of maximum likelihood (ML), of moments (MM), of probability weighted moments (PWM), and of generalized probability weighted moments (GPWM). When the shape parameter of the GPD is positive, the sample space is a finite interval whose upper bound depends on the distribution parameters. The MM, PWM and GPWM methods may produce estimates of this upper bound that are inconsistent with the observed data. This inconsistency occurs when one or more sample observations exceed the estimated upper bound, thus making this estimated upper bound physically unjustifiable. In this paper we shed more light on this problem of inconsistency with the data and examine its consequences by using Monte Carlo simulation. We provide new guidelines for choosing between the ML, MM, PWM and GPWM methods for estimating GPD quantiles.
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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 | 0.001 | 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 | 0.001 |
| 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".