Confidence Intervals for the Iwueze Distribution Parameter Using Bootstrap Techniques: Methodology and Application
Bibliographic record
Abstract
Abstract This paper proposes five bootstrap confidence intervals (CIs) for the parameter in the Iwueze distribution, a single-parameter mixture distribution combining the exponential and gamma distributions. The bootstrap CI using the normal approximation, percentile bootstrap CI, basic bootstrap CI, bootstrap-t CI, and bias-corrected and accelerated (BCa) bootstrap CI are introduced and evaluated through simulation studies and application to real datasets. The effectiveness of these methods is assessed in terms of the empirical coverage probability (ECP) and average width (AW) of the CIs in several situations. Through Monte Carlo simulations, the BCa bootstrap method was found to be the most reliable, providing accurate ECPs and making it a strong choice for situations where precise interval estimation is essential. On the other hand, the normal approximation method, though it produces narrower intervals, tends to have less accurate coverage, particularly with smaller sample sizes. This highlights the need to choose the method that best fits the specific goals of the study. Applying these methods to a real-world dataset further confirms their usefulness, offering dependable tools for statistical analysis. This research adds valuable insights to the field by improving the understanding of bootstrap techniques for the Iwueze distribution and offering practical advice on selecting methods to enhance the accuracy of statistical results.
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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 | 0.002 | 0.005 |
| 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".