Likelihood ratio order of the second spacing in multiple-outlier exponential models
Bibliographic record
Abstract
In this paper, we study the ordering properties of the second sample spacing arising from multiple-outlier exponential models in terms of the likelihood ratio order. Let X1,…,Xn [Y1,…,Yn] be independent exponential random variables with X1,…,Xp [Y1,…,Yp] having common hazard rate λ1 [λ1∗] and Xp+1,…,Xn [Yp+1,…,Yn] having common hazard rate λ2 [λ2∗]. Let D2:n and D2:n∗ denote the corresponding second sample spacing, respectively. It is proved here that D2:n is stochastically greater than D2:n∗ in the sense of the likelihood ratio order, under two different kinds of parameter conditions. The results established here strengthen and generalize some of the results known in the literature. Two applications are also presented to illustrate the results.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.014 | 0.085 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.002 | 0.007 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
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 source (direct Gemma or distilled Codex), 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".