Asymptotic and Bootstrap Confidence Intervals for the Ratio of Modes of Log-normal Distributions
Bibliographic record
Abstract
The log-normal distribution is essential for modeling positively skewed life-time data. Consequently, the log-normal distribution is used in numerous real-world situations. As a measure of central tendency, the mode corresponds to the most typical value within the data set. The goal of this paper is to estimate the confidence intervals (CIs) for the ratios of modes of two log-normal distributions using the asymptotic confidence interval ( $$CI_{Asym}$$ ) and three varieties of bootstrap confidence intervals ( $$CI_{t-boot},CI_{p-boot}$$ , and $$CI_{s-boot}$$ ). The effectiveness of the proposed CI methods is evaluated in terms of their coverage probabilities and average widths via Monte Carlo simulation. Lastly, the proposed CI methods were evaluated by applying them to real-world data on PM2.5 mass concentration in two areas of Thailand.
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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 | 0.003 |
| 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".