117,823 research outputs found
Further Analysis of the Zipf Law: Does the Rank-Size Rule Really Exist?
No full textThe widely-used Zipf law has two striking regularities: excellent fit and close-to-one exponent. When the exponent equals to one, the Zipf law collapses into the rank-size rule. This paper further analyzes the Zipf exponent. By changing the sample size, the truncation point, and the mix of cities in the sample, we found that the exponent is close to one only for some selected sub-samples. Using the values of estimated exponent from the rolling sample method, we obtained an elasticity of the exponent with respect to sample size.Zipf law; Rank-size rule; Rolling sample method
The size distribution of all Cambodian establishments
No full textThis paper presents empirical evidence on the size distribution of all Cambodian establishments in the nonfarm sector for 2009. Small- and large-scale establishments account for the largest share of employment, pointing to a “missing middle†that is commonly observed in developing countries. The analysis provides little evidence for Zipf’s law because Cambodian industry is characterized by a more dense mass of small establishments than the Zipf distribution would predict.Cambodia, Industry, Small and medium-scale enterprises, Employment, Size distribution, Establishments
The emergence of cities: complexity and urban dynamics
No full textThis paper presents an approach to urban dynamics that generalizes the traditionalrank-size model first popularized by Zipf (1949). It argues that we need to define the rate atwhich new cities emerge and old cities disappear within the apparent macro stability posed byZipf?s Law. We illustrate this with a reworking and extension of Zipf?s analysis of the USurban system, taking his analysis from 1790 to 1930 forward to the year 2000. In doing so, weintroduce a variety of devices to detect urban change based on traces through the rank-sizephase space, trajectories using a rank-time clock, and the definition of urban half-lives. We setthis analysis within the wider context of stochastic simulation that is currently dominatingdiscussion of scaling processes such as these
The size distribution of all Cambodian establishments
No full textThis paper describes the size distribution of all Cambodian establishments for 2009, showing that small- and large-scale establishments accounted for the largest share of employment. We find limited evidence for Zipf's law because Cambodian industry is characterized by a more dense mass of small establishments than the Zipf distribution would predict.Size distribution; establishments; Zipf's law; Cambodia
Zipfs Law for Cities: A Cross Country Investigation
No full textThis paper assesses the empirical validity of Zipf¿s Law for cities, using new data on 73countries and two estimation methods ¿ OLS and the Hill estimator. With either estimator,we reject Zipf¿s Law far more often than we would expect based on random chance; for 53out of 73 countries using OLS, and for 30 out of 73 countries using the Hill estimator. TheOLS estimates of the Pareto exponent are roughly normally distributed, but those of the Hillestimator are bimodal. Variations in the value of the Pareto exponent are better explained bypolitical economy variables than by economic geography variables.Cities, Zipf¿s Law, Pareto distribution, Hill estimator
LA CROISSANCE URBAINE CHINOISE RECONSIDÉRÉE
No full textOver the last decade, many researchers have focused on the study of different urban hierarchies and their evolution over time. These studies may or may not confirm Zipf’s law and emphasize the characteristics of urban growth. The question is then whether urban growth depends upon city-size or not, which is a main issue in modern regional economics. Using data on Chinese cities for the period 1960-2000, this paper aims to provide some answers to this question which has led to a recent passionate debate between the random growth theories and the endogenous growth theories.CROISSANCE URBAINE, HIÉRARCHIES URBAINES, LOI DE ZIPF, URBANISATION CHINOISE, AGGLOMÉRATION, LOI DE GIBRAT
Zipf's Law for Cities in the Regions and the Country
No full textThe salient rank-size rule known as Zipf's law is not only satisfied for Germany's national urban hierarchy, but also for the city size distributions in single German regions. To analyze this phenomenon, we build on the insights by Gabaix (1999) that Zipf's law follows from a stochastic growth process. In particular, Gabaix shows that if the regions follow Gibrat's law, we should observe Zipf at both the regional and the national level. This theory has never been addressed empirically. Using non-parametric techniques we find that Gibrat's law holds in each German region, irrespective of how "regions" are defined. In other words, Gibrat's law and therefore Zipf's law tend to hold everywhere in space.city size distributions, city growth, Zipf's law, Gibrat's law, rank-size rule
Measuring and modelling Internet diffusion using second level domains: the case of Italy
No full textThe last 10 years witnessed an exponential growth of the Internet. According to Hobbes' Internet Timeline, the Internet hosts are about 93 million, while in 1989 they were 100,000. The same happens for second level domain names. In July 1989 the registered domains were about 3,900 while they were over 2 million in July 2000. This paper reports about the construction of a database containing daily observations on registrations of second level domain names underneath the it ccTLD in order to analyse the diffusion of Internet among families and businesses. The section of the database referring to domains registered by individuals is analysed. The penetration rate over the relevant population of potential adopters is computed at highly disaggregated geographical level (province). A concentration analysis is carried out to investigate whether the geographical distribution of Internet is less concentrated than population and income suggesting a diffusive effect. Regression analysis is carried out using demographic, social, economic and infrastructure indicators. Finally we briefly describe the further developments of our research. At the present we are constructing a database containing domains registered by firms together with data about the registrants; the idea is to use this new database and the previous one in order to check for the existence of power laws both in the number of domains registered in each province and in the number of domains registered by each firm.Domain names, Internet metrics, Diffusion, Power laws, Zipf s law
Agents with dycotomic goals which generate a rank-size distribution
No full textMany explanations have been proposed for the rank-size rule or power law in city size
distribution based on a probabilistic process [4]. These explanations are usually opposed
to that proposed by Zipf [11] who explained the rank-size rule as the result of the application
of the principle of least effort. In his opinion, by using this principle, it is possible to
find an equilibrium between the two opposite forces of diversification and of unification.
In fact, because the main components of the system are resources, people and products,
the first force brings people near to resources, and the latter brings products near to
people. Even these notions are simple, and are accepted in the spatial economic field [5]
it is not clear how a rank-size rule can be derived from it[2].
In this paper I will show how a rank-size distribution can be generated by using multiagent
interaction which uses a probabilistic law to obtain opposing goals that correspond
to unification and diversification forces. This paper is divided in two sections: the first
section presents a model based on agents pursuing opposite goals; the second discusses
the model in relation to the previously proposed models
Exploring ice core drilling chips from a cold Alpine glacier for cosmogenic radionuclide (Be-10) analysis
No full textIce cores offer unique multi-proxy paleoclimate records, but provide only very limited sample material, which has to be carefully distributed for various proxy analyses. Beryllium-10, for example, is analysed in polar ice cores to investigate past changes of the geomagnetic field, solar activity, and the aerosol cycle, as well as to more accurately date the material. This paper explores the suitability of a drilling by-product, the so-called drilling chips, for 10Be-analysis. An ice core recently drilled at a cold Alpine glacier is used to directly compare 10Be-data from ice core samples with corresponding drilling chips. Both sample types have been spiked with 9Be-carrier and identically treated to chemically isolate beryllium. The resulting BeO has been investigated by accelerator mass spectrometry (AMS) for 10Be/9Be-ratios to calculate 10Be-concentrations in the ice. As a promising first result, four out of five sample-combinations (ice core and drilling chips) agree within 2-sigma uncertainty range. However, further studies are needed in order to fully demonstrate the potential of drilling chips for 10Be-analysis in alpine and shallow polar ice cores
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