Two‐component mixtures of normal, gamma, and Gumbel distributions for hydrological applications
Bibliographic record
Abstract
Whether mixtures of distributions are employed as a flexible modeling device to estimate densities or are used to model data thought to arise from several populations, they provide an efficient tool to approximate a distribution. Indeed, mixtures of distributions can model multiple modes, different types of skewness, etc., but they can also be employed to classify observations from heterogeneous data sets. In this paper, we study mixtures of distributions with normal, gamma, and Gumbel components. Moving away from the standard normal setting, gamma mixtures are developed in order to model strictly positive hydrological data and Gumbel mixtures for extreme variates. Since the data analyzed can exhibit dependency through time, we treat both the independent and dependent cases, where the latter is modeled through a Markov process. A fairly unified approach is adopted for the different distributions and the problem is treated from the Bayesian perspective, which enables us to use marginal densities to automatically compare the adequacy of the different models for a given data set. This model‐selection framework allows us to formally test the relevance of using mixture models by computing the marginal likelihoods of single distribution models and to verify the presence of a persistence in the time series by comparing independent and identically distributed (IID) and Markovian mixture models.
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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 | 0.031 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.003 | 0.004 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.004 |
| 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".