A Novel Class of Extreme Value Distributions Derived from the KM Transformation of the Generalized Extreme Value Distribution
Bibliographic record
Abstract
Modeling extreme events is crucial in various disciplines such as environmental sciences, hydrology, finance, and engineering. This paper introduces the KM-transformed Generalized Extreme Value (KMGEV) distribution, a novel and flexible model that generalizes the classical Generalized Extreme Value (GEV) distribution using the KM transformation framework recently proposed by Kavya and Manoharan. We derive the key statistical properties of the KMGEV distribution, including the probability density function (PDF), cumulative distribution function (CDF), survival function, hazard rate function, and quantile function. Additionally, we explore order statistics and their expected values. Parameter estimation is carried out via Maximum Likelihood Estimation (MLE) methods. Through Monte Carlo simulations, we investigate the impact of the shape parameter on moments such as skewness and kurtosis. Graphical analysis highlights the flexibility of the KMGEV model, suggesting its potential in modeling a variety of extreme value phenomena.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 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".