Parametric testing for normality against bimodal and unimodal alternatives using higher moments
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Bibliographic record
Abstract
This study examines population and small sample properties of the standardized fifth and sixth moments – the “higher moments” – for assessing univariate normality against bimodal and selected unimodal alternatives. Population parameters and distributions for selected bimodal mixtures are calculated and contrasted with those for the normal distribution. Using Gram-Charlier series expansion methods, an omnibus goodness of fit test incorporating the higher moments is specified and Monte Carlo simulation used to compare test power with parametric tests based on the standardized third and fourth sample moments: the asymptotic and size corrected versions of the Jarque-Bera score test and the omnibus D’Agostino K2 test. The studentized range and directional tests using the third through sixth moments are also considered. The results demonstrate that incorporating the fifth and sixth moments can provide enhanced parametric normality test power for bimodal normal mixture alternatives but not for various unimodal alternatives.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| 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