Bartlett-type correction for testing homogeneity of inverse Gaussian means
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Bibliographic record
Abstract
Similar to the normal distribution, the inverse Gaussian distribution has two parameters describing the location and the scale of the distribution. Hence, inverse Gaussian distribution is a convenient modelling alternative to the normal distribution. However, inference for homogeneity of means of k independent normal distributions is well established, whereas the same problem for k independent inverse Gaussian distributions is rarely discussed in the statistics literature. In this paper, the Studentization method is applied to obtain the marginal likelihood function for the mean parameter of the inverse Gaussian distribution. Then a Bartlett-type correction of the log likelihood ratio statistic obtained from the marginal likelihood function is proposed to test homogeneity of means of k independent inverse Gaussian distributions. Furthermore, by a slight modification of the proposed method, inference for the common mean parameter can also be accurately obtained. Simulation results indicate that the proposed method outperformed the existing methods.
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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 | 0.008 |
| 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