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 machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.035 | 0.246 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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 source (direct Gemma or distilled Codex), 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".