On Some Properties of Bivariate Exponential Distributions
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Bibliographic record
Abstract
We show that the two bivariate exponential distributions constructed in Bladt and Nielsen[ 5 Bladt , M. ; Nielsen , B.F. On the construction of bivariate exponential distributions with an arbitrary correlation coefficient . Stochastic Models 2010 , 26 ( 2 ), 295 – 308 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar] ] have the maximum and minimum correlation coefficients for any given order. We also generalize their constructions to the case where the matrix representations of the two (marginal) exponential distributions have different orders and show that the new constructions also have the maximum and minimum correlation coefficients. Our main tool is a majorization result for a special set of PH-generators.
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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 | 0.002 | 0.001 |
| 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 | 0.001 |
| Open science | 0.001 | 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