Enhancing inference for rama distribution: Confidence ntervals and their applications
Bibliographic record
Abstract
This research introduces and investigates four approaches for constructing confidence intervals (CIs) associated with the parameter of the Rama distribution—a model often applied in lifetime data modeling. The methods under consideration comprise the likelihood-based, Wald-type, bootstrap-t, and bias-corrected and accelerated (BCa) bootstrap intervals. To assess their practical utility, both Monte Carlo simulations and real data applications were utilized, emphasizing key performance indicators such as empirical coverage probability (ECP) and average width (AW) under various experimental conditions. To improve computational efficiency, a closed-form expression for the Wald-type CI was formulated. Simulation findings indicated that, across most situations, the ECPs obtained from both the likelihood-based and Wald-type CIs remained closely aligned with the nominal 95% confidence level. However, when the sample size was small, both the bootstrap-t and BCa bootstrap CIs yielded ECPs that fell short of the nominal level. As the sample size increased, the ECPs associated with these methods progressively approached the targeted confidence level, though variations in parameter values continued to influence their performance. The practical utility of these CIs was further validated through their application to two real-world datasets: monthly tax revenue in Egypt and plasma concentrations of indomethacin. The results from these applications were consistent with the findings of the simulation study, confirming the robustness and applicability of the proposed methods. Journal of Statistical Research 2025, Vol. 59, No. 1, pp. 107-129
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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 | 0.119 | 0.478 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.007 | 0.005 |
| Science and technology studies | 0.001 | 0.006 |
| Scholarly communication | 0.005 | 0.008 |
| Open science | 0.005 | 0.006 |
| Research integrity | 0.004 | 0.007 |
| 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".