ON THE NULL DISTRIBUTIONS OF THE ENTROPY TESTS FOR THE GAUSSIAN AND INVERSE GAUSSIAN MODELS*
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
ABSTRACT Vasicek Citation[1] used the "convolution of twelve uniforms" for a Monte Carlo tabulation of the 5% critical values for his entropy test for normality. We employ a superior normal generator to construct a corrected and extended tabulation for his test. Interestingly, it is shown that, the same tables can be used for implementing Mudholkar and Tian's Citation[2] entropy test for the composite inverse Gaussian hypothesis. The finding extends the known Gaussian, inverse Gaussian analogies. This article was published with incorrect figures in Communications in Statistics–-Theory and Methods, 30(8&9), pp. 1507–1520. The complete article with correct figures is reprinted here. Keywords: Vasicek testNormalityMaximum entropy Acknowledgments Notes This article was published with incorrect figures in Communications in Statistics–-Theory and Methods, 30(8&9), pp. 1507–1520. The complete article with correct figures is reprinted here.
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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 | 0.001 | 0.000 |
| 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