Classical and Bayesian Methods for Testing the Ratio of Variances of Delta-Lognormal Distributions
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Bibliographic record
Abstract
Six test statistics based on classical methods such as the generalized confidence interval (GCI), fiducial GCI (FGCI), and the method of variance estimates recovery (MOVER), as well as Bayesian methods using the highest posterior density (HPD) based on Jeffreys’ prior (HPD-Jef), Jeffreys’ rule prior (HPD-Rul), and the normal-gamma (HPD-NG) prior, for testing the ratio of variances of delta-lognormal distributions are proposed herein. A simulation study was conducted under several ratios of delta-lognormal variances to compare the performances of the proposed test statistics based on their empirical type I error rates and powers of the tests. The simulation results show that the MOVER test statistic performed well in terms of the empirical type I error rate for small sample sizes. In addition, the test statistics based on GCI, FGCI, and HPD-NG can be recommended for large sample sizes. When comparing the powers of the tests, the GCI and FGCI test statistics obtained higher powers than the others for moderate sample sizes while the HPD-NG test statistic achieved the highest power for large sample sizes. Daily rainfall amounts in the lower and upper northern regions of Thailand where the data follow delta-lognormal distributions were applied to illustrate the practical use of the proposed test statistics.
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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 | 0.004 | 0.017 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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