A study on statistical properties of a new class of $q$-Fréchet distribution
Bibliographic record
Abstract
This paper introduces the $ q $-Fréchet distribution, a two-parameter generalization of the classical Fréchet model that incorporates a pathway parameter $ q $ within the framework of Tsallis statistics. The proposed distribution offers enhanced flexibility for modeling real-world data with non-standard tail behavior, accommodating both sub-exponential ($ q<1 $) and super-exponential ($ 1<q<2 $) regimes. We derive its fundamental statistical properties, including survival, hazard, quantile, and moment functions, and investigate its extreme value behavior. Parameter estimation is addressed through multiple methods, with a focus on maximum likelihood and Bayesian inference, supported by a comprehensive simulation study. Applied to reliability datasets (carbon fiber strength and airborne transceiver repair times) the $ q $-Fréchet demonstrates a consistently superior fit compared to the classical Fréchet distribution, confirming its practical utility in modeling complex, heavy-tailed data. This work establishes the $ q $-Fréchet as a robust and adaptable model for applications in reliability engineering, survival analysis, and beyond.
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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 | 0.000 | 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".