A New Method for the Construction of Bivariate Archimedean Copulas Based on the λ Function
Bibliographic record
Abstract
We introduce and discuss a general method for constructing bivariate Archimedean copula families. The central item in our method is the function (t ∈ [0, 1]), where ϕ is the generator of the Archimedean copula. The construction of new copulas by means of λ has several advantages. The most important one is the straightforward relationship between the λ function and Kendall's τ and the coefficients of upper and lower tail dependence λ L and λ U , as defined in Joe (1997 Joe , H. ( 1997 ). Multivariate Models and Dependence Concepts . London : Chapman and Hall .[Crossref] , [Google Scholar]), which makes it possible to use these quantities as copula parameters and to control them independently of each other. Furthermore, the λ-method allows to construct multi-parameter families in a clear and organized way. The methodology is explained and illustrated by two- and three-parameter copula families.
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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 | 0.003 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.003 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.004 | 0.002 |
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".