Kinematics and dynamics of Pareto–Zipf's law and Gibrat's law

2004 ◽  
Vol 344 (1-2) ◽  
pp. 117-121 ◽  
Author(s):  
Hideaki Aoyama ◽  
Yoshi Fujiwara ◽  
Wataru Souma
Keyword(s):  
Zipf’S Law ◽  
Kinematics And Dynamics ◽  
Zipf's Law ◽  
Gibrat’S Law ◽  
Gibrat's Law

Growth and Firm Size Distribution

2016 ◽  
Vol 14 (2) ◽  
pp. 61-73
Author(s):  
Wei Zhang ◽  
Yan-Chun Zhu ◽  
Jian-Bo Wen ◽  
Yi-Jie Zhuang
Keyword(s):  
Size Distribution ◽  
Firm Size ◽  
Zipf’S Law ◽  
Growth Path ◽  
Firm Size Distribution ◽  
Zipf's Law ◽  
Gibrat’S Law ◽  
Gibrat's Law ◽  
Quantile Regression Method ◽  
The Relationship

Studies on the firm's size distribution (FSD) can set a good foundation to know about the growth path and mechanism of e-commerce firms. The purpose of this paper is to understand features of the China's listed e-commerce firms by testing Gibrat's law and Zipf's law within the Internet sectors. From a macroscopic perspective, with the approach of OLS estimation, Zipf's coefficient of the FSD is calculated to test whether Zipf's law holds. From a microscopic perspective, the relationship between e-commerce firm size and growth is explored by quantile regression method. The results indicate that from 2005 to 2014, Zipf's law cannot be rejected, with the relationship changing over time, Gibrat's law holds partly. It implies that competition status among China's e-commerce firms becomes more stable.

scholarly journals Investigation of urban regularities for Croatia in the period from 1857 to 2011

2020 ◽  
Vol 71 (4) ◽  
pp. 307-330
Author(s):  
Hrvoje Jošić ◽  
Berislav Žmuk
Keyword(s):  
Size Distribution ◽  
Unit Root ◽  
Urban Economics ◽  
Unit Roots ◽  
City Size ◽  
Zipf’S Law ◽  
Urban Hierarchy ◽  
Zipf's Law ◽  
Gibrat’S Law ◽  
Gibrat's Law

Two main regularities in the field of urban economics are Zipf’s law and Gibrat’s law. Zipf’s law states that distribution of largest cities should obey the Pareto rank-size distribution while Gibrat’s law states that proportionate growth of cities is independent of its size. These two laws are interconnected and therefore are often considered together. The objective of this paper is the investigation of urban regularities for Croatia in the period from 1857 to 2011. In order to estimate and evaluate the structure of Croatian urban hierarchy, Pareto or Zipf’s coefficients are calculated. The results have shown that the coefficient values for the largest settlements in different years are close to one, indicating that the Croatian urban hierarchy system follows the rank-size distribution and therefore obeys Zipf's law. The independence of city growth regarding the city size is tested using penal unit roots. Results for Gibrat's law testing using panel unit root tests have shown that there is a presence of unit root in growth of settlements therefore leading to the acceptance of Gibrat’s law.

scholarly journals From Gibrat’s law to Zipf’s law through cointegration?

2020 ◽  
Vol 192 ◽  
pp. 109211
Author(s):  
Lalanne Aurélie ◽  
Zumpe Martin
Keyword(s):  
Zipf’S Law ◽  
Zipf's Law ◽  
Gibrat’S Law ◽  
Gibrat's Law

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.

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