Cramér-von Mises and Anderson-Darling Goodness-of-Fit Tests for the Two-Parameter Kappa Distribution
Bibliographic record
Abstract
In hydrology, one often needs to use goodness-of-fit tests to describe how well a statistical frequency model fits a set of observations. The two-parameter kappa (KAP2) distribution is a frequency model that has already shown useful hydrological applications. The Cramér-von Mises and the Anderson-Darling tests are among the most frequently used goodness-of-fit tests in statistical practice. To apply these tests to the KAP2 distribution, statistical tables of critical values are needed. Such tables already exist for various other statistical distributions, but have not yet been developed for KAP2. This paper fills the gap by developing such tables for the KAP2 distribution. These tables are based on large sample theory, but correction formulas are also provided that make them applicable to small samples. KAP2 and the generalized Pareto distribution (GPD) are two subfamilies of the four-parameter kappa distribution that have been used in extreme value hydrological applications in the past. A detailed example is given that shows the usefulness of the KAP2 model for fitting some types of extreme hydrological data, and another example is provided to show how KAP2 may be used as an alternative to the GPD in certain extreme value applications.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.066 | 0.349 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.005 |
| Bibliometrics | 0.011 | 0.012 |
| Science and technology studies | 0.002 | 0.006 |
| Scholarly communication | 0.004 | 0.009 |
| Open science | 0.004 | 0.005 |
| Research integrity | 0.003 | 0.006 |
| Insufficient payload (model declined to judge) | 0.014 | 0.003 |
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".