An overview of goodness-of-fit tests for the Poisson distribution
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Bibliographic record
Abstract
The Poisson distribution has a large number of applications and is often used as a model in both a practical and a theoretical setting. As a result, various goodness-of-fit tests have been developed for this distribution. In this paper, we compare the finite sample power performance of ten of these tests against a wide range of alternative distributions for various sample sizes. The alternatives considered include, seemingly for the first time, weighted Poisson distributions. A number of additional tests are of historical importance although their power performance is not competitive against the remaining tests. These tests are discussed, but their powers are not included in the numerical analysis. The Monte Carlo study presented below indicates that the test with the best overall power performance is the test of Meintanis and Nikitin (2008), followed closely by the test of Rayner and Best (1990) (originally studied in Fisher, 1950).
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.005 |
| 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) | 0.000 | 0.000 |
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 it