Comparing Bootstrap Confidence Intervals for the Discrete Poisson–Bilal Distribution with Applications to Rainfall and Thunderstorms
Bibliographic record
Abstract
Abstract This paper presents a study on the application of bootstrap confidence intervals for the parameter of the discrete Poisson–Bilal distribution, which is a flexible model for over-dispersed count data. The discrete Poisson–Bilal distribution has been shown to provide a superior fit for various types of count data compared to traditional discrete distributions. This study compares three bootstrap confidence interval methods (percentile bootstrap, simple bootstrap, and bias-corrected and accelerated bootstrap) by using Monte Carlo simulations to assess their performance in terms of empirical coverage probability and average interval width. The study covers a range of sample sizes and parameter values, providing insights into the robustness and precision of each method. The results suggest that percentile bootstrap consistently offers narrower confidence intervals, particularly in small-sample scenarios, making it the preferred method. This research also demonstrates the application of these bootstrap confidence intervals to real meteorological data from Thailand and the USA, where the discrete Poisson–Bilal distribution provides an excellent fit. The findings confirm the practical reliability of bootstrap methods in estimating uncertainties for the discrete Poisson–Bilal distribution, with the percentile bootstrap method emerging as the most effective approach.
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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".