Optimal sample size for record data and associated cost analysis for exponential distribution
Bibliographic record
Abstract
Estimation of the mean of an exponential distribution based on record data has been treated by Samaniego and Whitaker [F.J. Samaniego, and L.R. Whitaker, On estimating popular characteristics from record breaking observations I. Parametric results, Naval Res. Logist. Quart. 33 (1986), pp. 531–543] and Doostparast [M. Doostparast, A note on estimation based on record data, Metrika 69 (2009), pp. 69–80]. When a random sample Y 1, …, Y n is examined sequentially and successive minimum values are recorded, Samaniego and Whitaker [F.J. Samaniego, and L.R. Whitaker, On estimating popular characteristics from record breaking observations I. Parametric results, Naval Res. Logist. Quart. 33 (1986), pp. 531–543] obtained a maximum likelihood estimator of the mean of the population and showed its convergence in probability. We establish here its convergence in mean square error, which is stronger than the convergence in probability. Next, we discuss the optimal sample size for estimating the mean based on a criterion involving a cost function as well as the Fisher information based on records arising from a random sample. Finally, a comparison between complete data and record is carried out and some special cases are discussed in detail.
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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 | 0.022 | 0.109 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.006 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.004 | 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 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".