On the Computation of Quantiles of Finite Mixtures with Stochastically Ordered Components
Bibliographic record
Abstract
Due to the lack of analytical expressions for the quantiles of finite mixture models, a reliable computational method is required for practical applications of mixture models. This paper focuses on numerical computations of quantiles of finite mixtures in which mixture components are stochastically ordered. As an alternative to single-step root-finding approaches, we propose a recursive algorithm in which, at each step, the quantile of the given mixture is expressed as the quantile of another mixture with one less component than the original mixture at a revised quantile level. To deal with numerical instability when the quantile level is close to either one or zero, we consider the forward, backward and combined methods for sequential updating. The proposed methods are illustrated with three size-biased mixture distributions: Erlang mixture, size-biased Weibull mixture and size-biased truncated lognromal mixture.
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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 | 0.000 |
| 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".