Theory of Zipf's Law and Beyond [recurso electrónico] / by Alex Saichev, Yannick Malevergne, Didier Sornette.

Por: Saichev, Alex [author.]Colaborador(es): Malevergne, Yannick [author.] | Sornette, Didier [author.] | SpringerLink (Online service)Tipo de material: TextoTextoSeries Lecture Notes in Economics and Mathematical Systems ; 632Editor: Berlin, Heidelberg : Springer Berlin Heidelberg, 2010Descripción: XII, 171p. 44 illus. online resourceTipo de contenido: text Tipo de medio: computer Tipo de portador: online resourceISBN: 9783642029462Tema(s): Economics | Distribution (Probability theory) | Economics, Mathematical | Finance | Economics/Management Science | Financial Economics | Probability Theory and Stochastic Processes | Game Theory/Mathematical MethodsFormatos físicos adicionales: Printed edition:: Sin títuloClasificación CDD: 332 Clasificación LoC:HG1-9999Recursos en línea: Libro electrónicoTexto
Contenidos:
Continuous Gibrat’s Law and Gabaix’s Derivation of Zipf’s Law -- Flow of Firm Creation -- Useful Properties of Realizations of the Geometric Brownian Motion -- Exit or “Death” of Firms -- Deviations from Gibrat’s Law and Implications for Generalized Zipf’s Laws -- Firm’s Sudden Deaths -- Non-stationary Mean Birth Rate -- Properties of the Realization Dependent Distribution of Firm Sizes -- Future Directions and Conclusions.
En: Springer eBooksResumen: Zipf's law is one of the few quantitative reproducible regularities found in economics. It states that, for most countries, the size distributions of city sizes and of firms are power laws with a specific exponent: the number of cities and of firms with sizes greater than S is inversely proportional to S. Zipf's law also holds in many other scientific fields. Most explanations start with Gibrat's law of proportional growth (also known as "preferential attachment'' in the application to network growth) but need to incorporate additional constraints and ingredients introducing deviations from it. This book presents a general theoretical derivation of Zipf's law, providing a synthesis and extension of previous approaches. The general theory is presented in the language of firm dynamics for the sake of convenience but applies to many other systems. It takes into account (i) time-varying firm creation, (ii) firm's exit resulting from both a lack of sufficient capital and sudden external shocks, (iii) the coupling between firm's birth rate and the growth of the value of the population of firms. The robustness of Zipf's law is understood from the approximate validity of a general balance condition. A classification of the mechanisms responsible for deviations from Zipf's law is also offered.
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Colección de Libros Electrónicos HG1 -9999 (Browse shelf(Abre debajo)) 1 No para préstamo 373489-2001

Continuous Gibrat’s Law and Gabaix’s Derivation of Zipf’s Law -- Flow of Firm Creation -- Useful Properties of Realizations of the Geometric Brownian Motion -- Exit or “Death” of Firms -- Deviations from Gibrat’s Law and Implications for Generalized Zipf’s Laws -- Firm’s Sudden Deaths -- Non-stationary Mean Birth Rate -- Properties of the Realization Dependent Distribution of Firm Sizes -- Future Directions and Conclusions.

Zipf's law is one of the few quantitative reproducible regularities found in economics. It states that, for most countries, the size distributions of city sizes and of firms are power laws with a specific exponent: the number of cities and of firms with sizes greater than S is inversely proportional to S. Zipf's law also holds in many other scientific fields. Most explanations start with Gibrat's law of proportional growth (also known as "preferential attachment'' in the application to network growth) but need to incorporate additional constraints and ingredients introducing deviations from it. This book presents a general theoretical derivation of Zipf's law, providing a synthesis and extension of previous approaches. The general theory is presented in the language of firm dynamics for the sake of convenience but applies to many other systems. It takes into account (i) time-varying firm creation, (ii) firm's exit resulting from both a lack of sufficient capital and sudden external shocks, (iii) the coupling between firm's birth rate and the growth of the value of the population of firms. The robustness of Zipf's law is understood from the approximate validity of a general balance condition. A classification of the mechanisms responsible for deviations from Zipf's law is also offered.

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