DIRICHLET-RELATED PROBABILITY PROBLEMS AND NEW TOOLS FOR SOLVING THEM
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
ABSTRACT In this paper we primarily consider waiting time problems under three different sampling rules. SR1 is the usual sampling with replacement, SR2 is without replacement, and SR3 is also with replacement, but uses no repetitions. We develop a new methodology for solving a wide variety of waiting time problems under each of the three sampling rules. A connection between waiting time problems under SR2 and SR3 is established which enables one to simultaneously solve waiting time problems under both of these sampling rules. The methods are illustrated with a large number of examples. Keywords: Dirichlet I, J, C, and D functionsWaiting time problemsGenerating functions ACKNOWLEDGMENTS The second author would like to thank the Natural Sciences and Engineering Research Council of Canada for funding this research. We would also like to thank the referee for comments that led to an improvement in the presentation of the paper.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.012 | 0.052 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 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 it