Moment-Based Approximation with Mixed Erlang Distributions
Why this work is in the frame
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Bibliographic record
Abstract
Moment-based approximations have been extensively analyzed over the years (see, e.g., Osogami and Harchol-Balter 2006 and references therein). A number of specific phase-type (and non phase-type) distributions have been considered to tackle the moment-matching problem (see, for instance, Johnson and Taaffe 1989). Motivated by the development of more flexible moment-based approximation methods, we develop and examine the use of finite mixture of Erlangs with a common rate parameter for the moment-matching problem. This is primarily motivated by Tijms (1994) who shows that this class of distributions can approximate any continuous positive distribution to an arbitrary level of accu-racy, as well as the tractability of this class of distributions for various problems of interest in quantitative risk management. We consider separately situations where the rate parameter is either known or unknown. For the former case, a direct connection with a discrete moment-matching problem is established. A parallel to the s-convex stochastic order (e.g., Denuit et al. 1998) is also drawn. Numerical examples are considered throughout.
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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 | 0.001 |
| 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 it