Ordering properties of the smallest and largest claim amounts in a general scale model
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Bibliographic record
Abstract
Suppose is a set of non-negative random variables with having the distribution function , for and are independent Bernoulli random variables, independent of the ’s, with , . Let , for . It is of interest to note that in actuarial science, corresponds to the claim amount in a portfolio of risks. In this paper, under certain conditions, by using the concept of vector majorization and related orders, we discuss stochastic comparison between the smallest claim amount in the sense of the usual stochastic and hazard rate orders. We also obtain the usual stochastic order between the largest claim amounts when the matrix of parameters changes to another matrix in a mathematical sense. We then apply the results for three special cases of the scale model: generalized gamma, Marshall–Olkin extended exponential and exponentiated Weibull distributions with possibly different scale parameters to illustrate the established results.
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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 | 0.000 |
| 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 | 0.000 | 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