An Algorithm for Fitting Heavy-Tailed Distributions via Generalized Hyperexponentials
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Bibliographic record
Abstract
In this paper, we propose an algorithm to fit heavy-tailed (HT) distribution functions by generalized hyperexponential (GH) distribution functions. A discussion of the steps, usage, and accuracy of the GH algorithm is given. Several examples in this paper show that the proposed method can be applied to fit HT distributions with a completely monotone probability density function (pdf) very well, like the Pareto distribution and the Weibull distribution with the shape parameter less than one, as well as HT distributions whose pdf is not completely monotone, like the lognormal distribution. In addition, we provide an example that shows that the proposed method can be applied to density estimation of real data presenting a heavy tail.
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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) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 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 it