Statistical Inference of Stress-Strength Reliability for Burr Distributions Based on Ranked Set Sampling
Bibliographic record
Abstract
A fundamental issue in several studies is the need for cost-effective sampling, particularly when measuring a significant characteristic is expensive, uncomfortable, or time-consuming. In terms of precision achieved per unit of sample, the ranked set sampling (RSS) approach offers a practical way to achieve observational economy. In the current work, ten frequentist estimation strategies are considered for the reliability of the stress strength parameter λ=P[T<Z], where T and Z are independent random variables following the Burr III and Burr XII distributions, respectively, that share the same shape parameter. Percentiles and weighted least squares, Anderson-Darling, maximum likelihood, minimum spacing absolute log distance, least squares, Cram’er-von Mises, maximum product of spacing, right-tailed Anderson-Darling, and minimum spacing absolute distance are some recommended estimation methods for the RSS and simple random sample methods. The effectiveness of the proposed RSS-based approximations is evaluated using simulation work employing certain accuracy standards. We conclude that the maximum product spacing and percentile approaches are the lowest in the mean squared error values for the reliability estimate when compared to those of the other alternatives. Two real data sets that trade share data and the prices of the 31 distinct children’s wooden toys are used to provide further findings.
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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 | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| 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".