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120
A Brief History of Generative Models for Power Law and Lognormal Distributions
 INTERNET MATHEMATICS
"... Recently, I became interested in a current debate over whether file size distributions are best modelled by a power law distribution or a a lognormal distribution. In trying ..."
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Cited by 420 (8 self)
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Recently, I became interested in a current debate over whether file size distributions are best modelled by a power law distribution or a a lognormal distribution. In trying
Zipf’s law for cities: An explanation
 Quart J Econ 1999
"... Zipf’s law is a very tight constraint on the class of admissible models of local growth. It says that for most countries the size distribution of cities strikingly fits a power law: the number of cities with populations greater than S is proportional to 1/S. Suppose that, at least in the upper tail, ..."
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Cited by 116 (1 self)
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Zipf’s law is a very tight constraint on the class of admissible models of local growth. It says that for most countries the size distribution of cities strikingly fits a power law: the number of cities with populations greater than S is proportional to 1/S. Suppose that, at least in the upper tail, all cities follow some proportional growth process (this appears to be verified empirically). This automatically leads their distribution to converge to Zipf’s law. I.
Predicting risksensitivity in humans and lower animals: Risk as variance or coefficient of variation
 Psychological Review
, 2004
"... This article examines the statistical determinants of risk preference. In a metaanalysis of animal risk preference (foraging birds and insects), the coefficient of variation (CV), a measure of risk per unit of return, predicts choices far better than outcome variance, the risk measure of normative ..."
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Cited by 91 (8 self)
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This article examines the statistical determinants of risk preference. In a metaanalysis of animal risk preference (foraging birds and insects), the coefficient of variation (CV), a measure of risk per unit of return, predicts choices far better than outcome variance, the risk measure of normative models. In a metaanalysis of human risk preference, the superiority of the CV over variance in predicting risk taking is not as strong. Two experiments show that people’s risk sensitivity becomes strongly proportional to the CV when they learn about choice alternatives like other animals, by experiential sampling over time. Experiencebased choices differ from choices when outcomes and probabilities are numerically described. Zipf’s law as an ecological regularity and Weber’s law as a psychological regularity may give rise to the CV as a measure of risk. Decision making under risk and uncertainty is a topic of research in disciplines as diverse as psychology, economics, zoology, and entomology. Both the animal and the human risky choice literatures have proposed models that either predict choices in a deterministic fashion or predict risk sensitivity (i.e., the probability of choosing a riskier or less risky option) in a stochastic fashion.
Riskbearing and the theory of income distribution
 Review of Economic Studies
, 1991
"... This paper develops the stochastic theory of distribution with a dynamic model which focuses on the role of incomplete insurance in generating inequality. Unlike previous work, our approach takes explicit account of the reason for market incompleteness in modeling agents' behaviour; in particul ..."
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Cited by 88 (4 self)
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This paper develops the stochastic theory of distribution with a dynamic model which focuses on the role of incomplete insurance in generating inequality. Unlike previous work, our approach takes explicit account of the reason for market incompleteness in modeling agents' behaviour; in particular, the amount of risk borne is endogenous. Using a model of growth with altruism in which agents are riskaverse and there is moral hazard, we show that lineage wealth follows a Markov process which converges globally to an ergodic distribution; this also represents the longrun population distribution of wealth. We discuss the role of particular assumptions, such as availability of production loans and unboundedness of utility, in yielding the qualitative properties of the distribution of wealth, the choice of "occupation", and the prevention of poverty traps. 1.
The evolution of city size distributions
 in V. Henderson and J.F. Thisse, eds, ‘Handbook of Regional and Urban Economics
, 2004
"... We review the accumulated knowledge on city size distributions and determinants of urban growth. This topic is of interest because of a number of key stylized facts, including notably Zipf’s law for cities (which states that the number of cities of size greater than S is proportional to 1/S) and the ..."
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Cited by 75 (12 self)
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We review the accumulated knowledge on city size distributions and determinants of urban growth. This topic is of interest because of a number of key stylized facts, including notably Zipf’s law for cities (which states that the number of cities of size greater than S is proportional to 1/S) and the importance of urban primacy. We first review the empirical evidence on the upper tail of city size distribution. We offer a novel discussion of the important econometric issues in the characterization of the distribution. We then discuss the theories that have been advanced to explain the approximate constancy of the distribution across very different economic and social systems, emphasizing both barebone statistical theories and more developed economic theories. We discuss the more recent work on the determinants of urban growth and, in particular, growth regressions, economic explanations of city size distributions other than Gibrat’s law, consequences of major
Persistent Inequality
 REVIEW OF ECONOMIC STUDIES
, 2003
"... When human capital accumulation generates pecuniary externalities across professions, and capital markets are imperfect, persistent inequality in utility and consumption is inevitable in any steady state. This is true irrespective of the degree of divisibility in investments. However, divisibility ( ..."
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Cited by 67 (11 self)
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When human capital accumulation generates pecuniary externalities across professions, and capital markets are imperfect, persistent inequality in utility and consumption is inevitable in any steady state. This is true irrespective of the degree of divisibility in investments. However, divisibility (or fineness of occupational structure) has implications for both the multiplicity and Paretoefficiency of steady states. Indivisibilities generate a continuum of inefficient and efficient steady states with varying per capita income. On the other hand, perfect divisibility typically implies the existence of a unique steady state distribution which is Paretoefficient.
The Double ParetoLognormal Distribution  A New Parametric Model for Size Distributions
, 2003
"... A family of probability densities, which has proved useful in modelling the size distributions of various phenomena, including incomes and earnings, human settlement sizes, oilfield volumes and particle sizes, is introduced. ..."
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Cited by 56 (2 self)
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A family of probability densities, which has proved useful in modelling the size distributions of various phenomena, including incomes and earnings, human settlement sizes, oilfield volumes and particle sizes, is introduced.
income tax rates and economic growth in developing countries
 European Economic Review
, 1993
"... One step closer to being able to do the empirical work needed on the common hypothesis of growth theory: that income taxes have a negative effect on the pace of economic expansion. Policy Research Wo*ing Pap Ia disaeminatethefindings of work in pogrss and encouage the exchange of ideas among Bank st ..."
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Cited by 38 (3 self)
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One step closer to being able to do the empirical work needed on the common hypothesis of growth theory: that income taxes have a negative effect on the pace of economic expansion. Policy Research Wo*ing Pap Ia disaeminatethefindings of work in pogrss and encouage the exchange of ideas among Bank staff and allothers interesed in devdopment issucs.Thesepapas, distributed by theResearch Advisory Staff, carry thenames ofthe authors, reflect only thdirviews, andshouldbeused and citedaccordingly.Thefindings, intepeations,andcondcusions arethe authors'own.Theyshould not be attubuted to the Wodd Bank, its Board of Dirctor, is managememn, or any of its member countries. Pu bl ic Di sc lo su re A ut ho riz ed Pu bl ic Di sc lo su re A ut ho riz ed Pu bl ic Di sc lo su re A ut ho riz ed Pu bl ic Di sc lo su re A ut ho riz ed
The emergence of hierarchy in transportation networks
 Annals of Regional Science
, 2005
"... A transportation network is a complex system that exhibits the properties of selforganization and emergence. Previous research in dynamics related to transportation networks focuses on traffic assignment or traffic management. This research concentrates on the dynamics of the orientation of major ro ..."
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Cited by 34 (17 self)
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A transportation network is a complex system that exhibits the properties of selforganization and emergence. Previous research in dynamics related to transportation networks focuses on traffic assignment or traffic management. This research concentrates on the dynamics of the orientation of major roads in a network and abstractly models these dynamics to understand the basic properties of transportation networks. A model is developed to capture the dynamics that leads to a hierarchical arrangement of roads for a given network structure and land use distribution. Localized investment rules – revenue produced by traffic on a link is invested for that link’s own development – are employed. Under reasonable parameters, these investment rules, coupled with traveler behavior, and underlying network topology result in the emergence of a hierarchical pattern. Hypothetical networks subject to certain conditions are tested with this model to explore the network properties. Though hierarchies seem to be designed by planners and engineers, the results show that they are intrinsic properties of networks. Also, the results show that roads, specific routes with continuous attributes, are emergent properties of transportation networks.
On the Distribution of City Sizes
, 2003
"... The city size distribution of many countries is remarkably well approximated by a Pareto distribution. We study what constraints this regularity imposes on standard urban models. We find that under general conditions urban models must have (i) a balanced growth path and (ii) a Pareto distribution fo ..."
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Cited by 27 (0 self)
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The city size distribution of many countries is remarkably well approximated by a Pareto distribution. We study what constraints this regularity imposes on standard urban models. We find that under general conditions urban models must have (i) a balanced growth path and (ii) a Pareto distribution for the underlying source of randomness. In particular, one of the following combinations can induce a Pareto distribution of city sizes: (i) preferences for different goods follow reflected random walks, and the elasticity of substitution between goods is 1; or (ii) total factor productivities in the production of different goods follow reflected random walks, and increasing returns are equal across goods.