Bivariate Models Constructed by the Marginal Transformation Method: With Applications in Hydrology
Bibliographic record
Abstract
The analysis of two dependent hydrological variables, X and Y, is a common problem in hydrology. These variables often have marginal distributions that do not belong to the same distribution family. They also often belong to the class of extreme hydrological variables. The use of copulas for bivariate frequency modeling has been advanced as an attractive tool for hydrologists because it allows modeling two related variables, irrespective of their marginal distributions. However, the class of bivariate models commonly used in hydrology has been restrictive. It has in fact ignored an important class of models which, like those obtained from copulas, can have marginal distributions that do not belong to the same family. We present some recent research on this class of bivariate models, and illustrate their use through an application. Our results show that these models need to be given more attention. The application provided will also show how such models, as well as those constructed from copulas, can be useful in dealing with incomplete data in hydrology. With incomplete data, it will be shown how the information contained in a hydrological series of longer length (X) can be utilized to enhance the quality of the quantile estimates for another (associated) series of shorter length (Y).
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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 | 0.004 | 0.016 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 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 | 0.001 |
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".