Two Universality Properties Associated with the Monkey Model of Zipf’s Law
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Bibliographic record
Abstract
The distribution of word probabilities in the monkey model of Zipf’s law is associated with two universality properties: (1) the exponent in the approximate power law approaches −1 as the alphabet size increases and the letter probabilities are specified as the spacings from a random division of the unit interval for any distribution with a bounded density function on [0,1] ; and (2), on a logarithmic scale the version of the model with a finite word length cutoff and unequal letter probabilities is approximately normally distributed in the part of the distribution away from the tails. The first property is proved using a remarkably general limit theorem from Shao and Hahn for the logarithm of sample spacings constructed on [0,1] and the second property follows from Anscombe’s central limit theorem for a random number of independent and identically distributed (i.i.d.) random variables. The finite word length model leads to a hybrid Zipf-lognormal mixture distribution closely related to work in other areas.
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Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| 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 | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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