Zipf's Law for Firms: Relevance of Birth and Death Processes

2008 ◽  
Author(s):  
Yannick Malevergne ◽  
Alexander I. Saichev ◽  
Didier Sornette
Keyword(s):  
Zipf’S Law ◽  
Birth And Death Processes ◽  
Zipf's Law

ZIPF AND LERCH LIMIT OF BIRTH AND DEATH PROCESSES

2009 ◽  
Vol 24 (1) ◽  
pp. 129-144 ◽  
Author(s):  
B. Klar ◽  
P. R. Parthasarathy ◽  
N. Henze
Keyword(s):  
Chemical Kinetics ◽  
Continued Fractions ◽  
Zipf’S Law ◽  
Death Process ◽  
Speed Of Convergence ◽  
Birth And Death Process ◽  
Birth And Death Processes ◽  
Zipf's Law ◽  
Wide Range ◽  
Epidemiology Data

Birth and death processes are useful in a wide range of disciplines from computer networks and telecommunications to chemical kinetics and epidemiology. Data from many different areas such as linguistics, music, or warfare fit Zipf's law surprisingly well. The Lerch distribution generalizes Zipf's law and is applicable in survival and dispersal processes. In this article we construct a birth and death process that converges to the Lerch distribution in the limit as time becomes large, and we investigate the speed of convergence. This is achieved by employing continued fractions. Numerical illustrations are presented through tables and graphs.

scholarly journals Types, Tokens, and Hapaxes: A New Heap’s Law

Glottotheory ◽  
2019 ◽  
Vol 9 (2) ◽  
pp. 113-129
Author(s):  
Victor Davis
Keyword(s):  
First Principles ◽  
Scaling Law ◽  
Written Language ◽  
Zipf’S Law ◽  
Academic Press ◽  
Zipf's Law ◽  
New Words ◽  
Size Dependent ◽  
Link Type ◽  
Combinatorial Model

Abstract Heap’s Law https://dl.acm.org/citation.cfm?id=539986 Heaps, H S 1978 Information Retrieval: Computational and Theoretical Aspects (Academic Press). states that in a large enough text corpus, the number of types as a function of tokens grows as N = K{M^\beta } for some free parameters K, \beta . Much has been written http://iopscience.iop.org/article/10.1088/1367-2630/15/9/093033 Font-Clos, Francesc 2013 A scaling law beyond Zipf’s law and its relation to Heaps’ law (New Journal of Physics 15 093033)., http://iopscience.iop.org/article/10.1088/1367-2630/11/12/123015 Bernhardsson S, da Rocha L E C and Minnhagen P 2009 The meta book and size-dependent properties of written language (New Journal of Physics 11 123015)., http://iopscience.iop.org/article/10.1088/1742-5468/2011/07/P07013 Bernhardsson S, Ki Baek and Minnhagen 2011 A paradoxical property of the monkey book (Journal of Statistical Mechanics: Theory and Experiment, Volume 2011)., http://milicka.cz/kestazeni/type-token_relation.pdf Milička, Jiří 2009 Type-token & Hapax-token Relation: A Combinatorial Model (Glottotheory. International Journal of Theoretical Linguistics 2 (1), 99–110)., https://www.nature.com/articles/srep00943 Petersen, Alexander 2012 Languages cool as they expand: Allometric scaling and the decreasing need for new words (Scientific Reports volume 2, Article number: 943). about how this result and various generalizations can be derived from Zipf’s Law. http://dx.doi.org/10.1037/h0052442 Zipf, George 1949 Human behavior and the principle of least effort (Reading: Addison-Wesley). Here we derive from first principles a completely novel expression of the type-token curve and prove its superior accuracy on real text. This expression naturally generalizes to equally accurate estimates for counting hapaxes and higher n-legomena.

scholarly journals Dynamical approach to Zipf's law

2021 ◽  
Vol 3 (1) ◽  
Author(s):  
Giordano De Marzo ◽  
Andrea Gabrielli ◽  
Andrea Zaccaria ◽  
Luciano Pietronero
Keyword(s):  
Zipf’S Law ◽  
Zipf's Law ◽  
Dynamical Approach

Optimization of morpheme length: a cross-linguistic assessment of Zipf’s and Menzerath’s laws

2021 ◽  
Vol 7 (s3) ◽  
Author(s):  
Matthew Stave ◽  
Ludger Paschen ◽  
François Pellegrino ◽  
Frank Seifart
Keyword(s):  
Structural Information ◽  
Unit Length ◽  
Zipf’S Law ◽  
Zipf's Law ◽  
Linguistic Structure ◽  
Morphological Complexity ◽  
Linguistic Assessment ◽  
Linguistic Units

Abstract Zipf’s Law of Abbreviation and Menzerath’s Law both make predictions about the length of linguistic units, based on corpus frequency and the length of the carrier unit. Each contributes to the efficiency of languages: for Zipf, units are more likely to be reduced when they are highly predictable, due to their frequency; for Menzerath, units are more likely to be reduced when there are more sub-units to contribute to the structural information of the carrier unit. However, it remains unclear how the two laws work together in determining unit length at a given level of linguistic structure. We examine this question regarding the length of morphemes in spoken corpora of nine typologically diverse languages drawn from the DoReCo corpus, showing that Zipf’s Law is a stronger predictor, but that the two laws interact with one another. We also explore how this is affected by specific typological characteristics, such as morphological complexity.

Analysis of Zipf's law: An index approach

1987 ◽  
Vol 23 (3) ◽  
pp. 171-182 ◽  
Author(s):  
Ye-Sho Chen ◽  
Ferdinand F. Leimkuhler
Keyword(s):  
Zipf’S Law ◽  
Zipf's Law ◽  
Index Approach

scholarly journals Emergence of Zipf’s law in the evolution of communication

2011 ◽  
Vol 83 (3) ◽  
Author(s):  
Bernat Corominas-Murtra ◽  
Jordi Fortuny ◽  
Ricard V. Solé
Keyword(s):  
Zipf’S Law ◽  
Zipf's Law ◽  
Evolution Of Communication

A Time-Series Audit of Zipf's Law as a Measure of Terrane Endowment and Maturity in Mineral Exploration

2011 ◽  
Vol 106 (2) ◽  
pp. 241-259 ◽  
Author(s):  
P. Guj ◽  
M. Fallon ◽  
T. C. McCuaig ◽  
R. Fagan
Keyword(s):  
Time Series ◽  
Mineral Exploration ◽  
Zipf’S Law ◽  
Zipf's Law

Physical complexity and Zipf's law

1992 ◽  
Vol 31 (3) ◽  
pp. 525-543 ◽  
Author(s):  
R. G�nther ◽  
B. Schapiro ◽  
P. Wagner
Keyword(s):  
Zipf’S Law ◽  
Zipf's Law ◽  
Physical Complexity
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