ON A CLASS OF GENERALIZED MARSHALL–OLKIN BIVARIATE DISTRIBUTIONS AND SOME RELIABILITY CHARACTERISTICS
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Bibliographic record
Abstract
We consider here a general class of bivariate distributions from reliability point of view, and refer to it as generalized Marshall–Olkin bivariate distributions. This class includes as special cases the Marshall–Olkin bivariate exponential distribution and the class of bivariate distributions studied recently by Sarhan and Balakrishnan [25]. For this class, the reliability, survival, hazard, and mean residual life functions are all derived, and their monotonicity is discussed for the marginal as well as the conditional distributions. These functions are also studied for the series and parallel systems based on this bivariate distribution. Finally, the Clayton association measure for this bivariate model is derived in terms of the hazard gradient.
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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 | 0.002 |
| 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