TY - BOOK ID - 14304953 TI - Theory of Zipf's Law and Beyond AU - Saichev, Alexander I. AU - Malevergne, Yannick. AU - Sornette, Didier. PY - 2010 SN - 3642029469 3642029450 3642029477 9786612832673 1282832670 PB - Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, DB - UniCat KW - Cities and towns -- Growth -- Mathematical models. KW - Economic geography -- Mathematical models. KW - Urban economics -- Mathematical models. KW - Zipf’s law. KW - Urban economics KW - Economic geography KW - Zipf's law KW - Cities and towns KW - Sociology & Social History KW - Finance KW - Business & Economics KW - Economic History KW - Finance - General KW - Communities - Urban Groups KW - Social Sciences KW - Mathematical models KW - Growth KW - Zipf's law. KW - Mathematical models. KW - Geographic models KW - Probabilities. KW - Economic theory. KW - Macroeconomics. KW - Economics. KW - Macroeconomics/Monetary Economics//Financial Economics. KW - Probability Theory and Stochastic Processes. KW - Economic Theory/Quantitative Economics/Mathematical Methods. KW - Language and languages KW - Word frequency KW - Distribution (Probability theory. KW - Economics KW - Economic theory KW - Political economy KW - Social sciences KW - Economic man KW - Distribution functions KW - Frequency distribution KW - Characteristic functions KW - Probabilities KW - Probability KW - Statistical inference KW - Combinations KW - Mathematics KW - Chance KW - Least squares KW - Mathematical statistics KW - Risk UR - https://www.unicat.be/uniCat?func=search&query=sysid:14304953 AB - 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. ER -