On the Convergence of Hypergeometric to Binomial Distributions
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
This study presents a measure-theoretic approach to estimate the upper bound on the total variation of the difference between hypergeometric and binomial distributions using the Kullback-Leibler information divergence. The binomial distribution can be used to find the probabilities associated with the binomial experiments. But if the sample size is large relative to the population size, the experiment may not be binomial, and a binomial distribution is not a good choice to find the probabilities associated with the experiment. The hypergeometric probability distribution is the appropriate probability model to be used when the sample size is large compared to the population size. An upper bound for the total variation in the distance between the hypergeometric and binomial distributions is derived using only the sample and population sizes. This upper bound is used to demonstrate how the hypergeometric distribution uniformly converges to the binomial distribution when the population size increases relative to the sample size.
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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| 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 it