Confidence Estimation of the Ratio of Variances of Two Log-normal Populations
Bibliographic record
Abstract
This study investigates asymptotic and bootstrap confidence intervals (CIs) for the ratio of variances of two independent log-normal distributions. Extensive simulations were conducted to evaluate the performance of these CIs under varying sample sizes (10 to 350) and variance ratios, with one variance fixed at 0.1 and the other varying from 0.1 to 2.0. The impacts of balanced and unbalanced designs on sample size were studied. The results reveal that the asymptotic CI performs well for small variance differences, especially with moderate to large sample sizes, while bootstrap CIs outperform it for larger variance differences. Notably, the $$t$$ -bootstrap CI excels when both the variance difference and sample sizes are large, whereas the percentile and standard bootstrap CIs are preferable for small variance differences. The study also demonstrates the practical application of these methods using PM2.5 mass concentration data from two industrial sites in Thailand, confirming their effectiveness in real-world scenarios.
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How this classification was reachedexpand
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 | 0.001 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".