Log-concavity of the extremes from Gumbel bivariate exponential distributions
Bibliographic record
Abstract
In the classical risk theory, it is often used that different type dimensions can be aggregated into a single-dimensional statistic, as well as the assumption of properties on log-concavity of this aggregation. The extreme-order statistics, minimum and maximum, might be used as aggregate statistics. In this paper, we discuss the log-concavity of the survival function of the minimum and maximum from Gumbel bivariate exponential models, through the log-concavity of generalized mixtures of four or fewer exponential distributions, extending the papers of Baggs and Nagaraja [Baggs, G.E. and Nagaraja, H.N., 1996, Reliability properties of order statistics from bivariate exponential distributions. Communications in Statistics—Stochastic Models, 12, 611–631] and Franco and Vivo [Franco, M. and Vivo, J.M., 2002, Reliability properties of series and parallel systems from bivariate exponential models. Communications in Statistics—Theory and Methods, 31, 2349–2360] devote to the log-concavity for generalized mixtures of three or fewer exponential distributions.
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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 | 0.008 | 0.045 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.004 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".