Two Universality Properties Associated with the Monkey Model of Zipf’s Law
AbstractThe 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. View Full-Text
Scifeed alert for new publicationsNever miss any articles matching your research from any publisher
- Get alerts for new papers matching your research
- Find out the new papers from selected authors
- Updated daily for 49'000+ journals and 6000+ publishers
- Define your Scifeed now
Perline, R.; Perline, R. Two Universality Properties Associated with the Monkey Model of Zipf’s Law. Entropy 2016, 18, 89.
Perline R, Perline R. Two Universality Properties Associated with the Monkey Model of Zipf’s Law. Entropy. 2016; 18(3):89.Chicago/Turabian Style
Perline, Richard; Perline, Ron. 2016. "Two Universality Properties Associated with the Monkey Model of Zipf’s Law." Entropy 18, no. 3: 89.
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.