Confidence Intervals for the Parameter in the Kpenadidum Distribution: Comparative Evaluation and Real-World Application
Bibliographic record
Abstract
In this article, we propose four confidence intervals (CIs) for parameter estimation of the Kpenadidum distribution, which is applied in lifetime data analysis. We developed and evaluated different types of CIs, including likelihood-based, Wald-type, bootstrap- $$t$$ , and bias-corrected accelerated bootstrap CIs. The comparison was conducted using a simulation study and an application with a real data set. These CIs were evaluated based on their empirical coverage probability (ECP) and average width (AW) across various situations. Furthermore, we derived the explicit formula for computing the Wald-type CI, which simplifies the computation. The results show that the ECPs of the likelihood-based and Wald-type CIs tend to converge toward the nominal confidence level of 0.95 in almost all situations. When the sample size is small ( $$n=10$$ , 20, or 30), the bootstrap- $$t$$ and BCa bootstrap CIs produce ECPs less than 0.95. As the sample sizes increase, the ECPs of the bootstrap- $$t$$ and BCa bootstrap CIs tend to approach the nominal confidence level. Additionally, the parameter values impact the ECP. At low parameter values, the CPs are quite close to the nominal confidence level, with the likelihood-based and Wald-type CIs achieving an ECP of approximately 0.95. However, the ECPs for the bootstrap- $$t$$ and BCa bootstrap CIs tend to have lower coverage at higher parameter values with small sample sizes. We confirmed the efficacy of the CIs by applying them to the monthly tax revenue in Egypt, and the results matched those from the simulation study.
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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 | 0.003 | 0.002 |
| 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".