Distribution-free confidence intervals for quantiles and tolerance intervals in terms of <i>k</i> -records
Bibliographic record
Abstract
In this paper, we consider the problem of determining non-parametric confidence intervals for quantiles when available data are in the form of k-records. Distribution-free confidence intervals as well as lower and upper confidence limits are derived for fixed quantiles of an arbitrary unknown distribution based on k-records of an independent and identically distributed sequence from that distribution. The construction of tolerance intervals and limits based on k-records is also discussed. An exact expression for the confidence coefficient of these intervals are derived. Some tables are also provided to assist in choosing the appropriate k-records for the construction of these confidence intervals and tolerance intervals. Some simulation results are presented to point out some of the features and properties of these intervals. Finally, the data, representing the records of the amount of annual rainfall in inches recorded at Los Angeles Civic Center, are used to illustrate all the results developed in this paper and also to demonstrate the improvements that they provide on those based on either the usual records or the current records.
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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 | 0.046 | 0.334 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.005 | 0.006 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.005 | 0.008 |
| Open science | 0.005 | 0.003 |
| Research integrity | 0.002 | 0.005 |
| 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".