Confidence Intervals for the Ratio of Means of Two Independent Log-Normal Distributions
Bibliographic record
Abstract
In this paper, we investigate confidence intervals for the ratio of means of two independent lognormal distributions. The normal approximation (NA) approach was proposed. We compared the proposed with another approaches, the ML, GCI, and MOVER. The performance of these approaches were evaluated in terms of coverage probabilities and interval widths. The Simulation studies and results showed that the GCI and MOVER approaches performed similar in terms of the coverage probability and interval width for all sample sizes. The ML and NA approaches provided the coverage probability close to nominal level for large sample sizes. However, our proposed method provided the interval width shorter than other methods. Overall, our proposed is conceptually simple method. We recommend that our proposed approach is appropriate for large sample sizes because it is consistently performs well in terms of the coverage probability and the interval width is typically shorter than the other approaches. Finally, the proposed approaches are illustrated using a real-life example.
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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 | 0.034 | 0.242 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.006 | 0.004 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.004 | 0.005 |
| Open science | 0.004 | 0.003 |
| Research integrity | 0.003 | 0.004 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".