Statistical Analysis for the Unit Exponential Distribution Under Ranked Set Sampling with Applications to Engineering Data
Bibliographic record
Abstract
In numerous research endeavors, cost-effective sampling is paramount, particularly when measuring the feature of interest is costly, intrusive, or requires a lot of time. Ranked set sampling (RSS) offers a valuable approach to optimize observational efficiency and enhance data collection. The two-parameter unit exponential distribution (UED) has emerged as a valuable tool for analyzing asymmetrical complex datasets. Its density function can exhibit various right-skewed and left-skewed shapes, making it well-suited for modeling a wide range of data. In this study, RSS is used to investigate the performance of ten classical estimation techniques for the UED parameters. Using a variety of accuracy criteria, the suggested RSS-based estimators’ performance was compared to that of simple random sampling (SRS) through a simulation study. Partial and overall rankings of the estimators were computed to identify the best estimate approach. As evidenced by simulation studies, the maximum likelihood and maximum product spacing methods demonstrate significant promise in accurately assessing the estimated quality of RSS and SRS, respectively. Due to its higher efficiency compared to SRS, RSS demonstrates superior performance in terms of mean squared error and other relevant metrics. Two practical implementations support our findings. The first set of data examines the performance and dependability of 20 components by focusing on their failure times. The second data explores the proportion of crude oil converted to gasoline, assessing its efficiency in the refining process. By effectively analyzing both failure time data and the proportion of crude oil data, industries can make informed decisions, improve efficiency, and optimize their operations.
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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 | 0.060 | 0.160 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.003 |
| Bibliometrics | 0.004 | 0.004 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.004 | 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".