Log-concavity of the extremes from Gumbel bivariate exponential distributions
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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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Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 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 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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