Stochastic inequalities involving past extropy of order statistics and past extropy of record values
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
<abstract><p>Recently, extropy has emerged as an alternative measure of uncertainty instead of entropy. When it comes to quantifying uncertainty regarding the remaining lifetime of a component, entropy has proven to be less effective. Therefore, the concept of residual entropy was introduced to address this limitation. Similar to the residual entropy, the residual extropy was formulated and used to investigate the uncertainty in the residual lifetime of a unit. Systems in the real world exhibit a pervasive property of uncertainty that affects future events and past events. For this reason, the concept of past extropy was introduced to specifically capture and analyze the uncertainty associated with past events. This paper focuses on stochastic aspects, including stochastic orderings, which provide useful inequalities related to past extropy when applied to order statistics and lower record values. It is worth noting that the past extropy of the $ i $th-order statistics and record values in the continuous case is related to the past extropy of the $ i $th-order statistics and record values evaluated from the uniform distribution. The monotonicity of the past extropy of order statistics is examined and some insights into the past extropy of lower data set values are also given. Finally, some computational results are presented. In fact, an estimator for the extropy of the exponential distribution is proposed. For this purpose, the maximum likelihood estimator is derived. The proposed method is easy to implement and apply from a computational point of view.</p></abstract>
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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 | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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) | 0.000 | 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