Calculation of Precise Constants in a Probability Model of Zipf’s Law Generation and Asymptotics of Sums of Multinomial Coefficients
Joint Authors
Bochkarev, Vladimir
Lerner, Eduard
Source
International Journal of Mathematics and Mathematical Sciences
Issue
Vol. 2017, Issue 2017 (31 Dec. 2017), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2017-05-07
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
Let ω0,ω1,…,ωn be a full set of outcomes (symbols) and let positive pi, i=0,…,n, be their probabilities (∑i=0npi=1).
Let us treat ω0 as a stop symbol; it can occur in sequences of symbols (we call them words) only once, at the very end.
The probability of a word is defined as the product of probabilities of its symbols.
We consider the list of all possible words sorted in the nonincreasing order of their probabilities.
Let pr be the probability of the rth word in this list.
We prove that if at least one of the ratios logpi/logpj, i,j∈1,…,n, is irrational, then the limit limr→∞pr/r-1/γ exists and differs from zero; here γ is the root of the equation ∑i=1npiγ=1.
The limit constant can be expressed (rather easily) in terms of the entropy of the distribution (p1γ,…,pnγ).
American Psychological Association (APA)
Bochkarev, Vladimir& Lerner, Eduard. 2017. Calculation of Precise Constants in a Probability Model of Zipf’s Law Generation and Asymptotics of Sums of Multinomial Coefficients. International Journal of Mathematics and Mathematical Sciences،Vol. 2017, no. 2017, pp.1-11.
https://search.emarefa.net/detail/BIM-1167770
Modern Language Association (MLA)
Bochkarev, Vladimir& Lerner, Eduard. Calculation of Precise Constants in a Probability Model of Zipf’s Law Generation and Asymptotics of Sums of Multinomial Coefficients. International Journal of Mathematics and Mathematical Sciences No. 2017 (2017), pp.1-11.
https://search.emarefa.net/detail/BIM-1167770
American Medical Association (AMA)
Bochkarev, Vladimir& Lerner, Eduard. Calculation of Precise Constants in a Probability Model of Zipf’s Law Generation and Asymptotics of Sums of Multinomial Coefficients. International Journal of Mathematics and Mathematical Sciences. 2017. Vol. 2017, no. 2017, pp.1-11.
https://search.emarefa.net/detail/BIM-1167770
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1167770