Ordered Random Variables from Discontinuous Distributions
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Bibliographic record
Abstract
In the absolutely continuous case, order statistics, record values and several other models of ordered random variables can be viewed as special cases of generalized order statistics, which enables a unified treatment of their theory. This paper deals with discon- tinuous generalized order statistics, continuing on the recent work of Tran (2006). Specifically, we show that in general neither records nor weak records are submodels of discrete generalized order statistics. Next, we show that progressively Type-II right censored order statis- tics from an arbitrary distribution can be embedded in the model of generalized order statistics and then use this fact to establish some distributional properties of progressively Type-II right censored order statistics. Finally, we present some characterizations of the geomet- ric distribution based on progressively Type-II right censored order statistics.
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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 | 0.003 |
| 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) | 0.001 | 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