A Look at the Primary Order Preserving Properties of Stochastic Orders: Theorems, Counterexamples and Applications in Cognitive Psychology
Bibliographic record
Abstract
In this paper, we prove that for a set of ten univariate stochastic orders including the usual order, a univariate stochastic order preserves either both, one or none of additivity and multiplication properties over the vector space of real-valued random variables. Then, classifying participant’s quickness in a mental chronometry trial to “weakly faster” and “strongly faster”, we use the above results for the usual stochastic order to establish necessary and sufficient conditions for a participant to be strongly faster than the other in terms of the fitted Wald, Exponentially modified Wald(ExW), and Exponentially modified Gaussian(ExG) distributional parameters. This research field remains uncultivated for other univariate stochastic orders and in several directions.
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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 | 0.013 | 0.040 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.002 | 0.013 |
| Scholarly communication | 0.003 | 0.010 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.004 |
| Insufficient payload (model declined to judge) | 0.003 | 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 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".