Theory of Zipf's Law and Beyond (Lecture Notes in Economics and Mathematical Systems, Band 632) Saichev Alexander, I., Yannick Malevergne and Didier Sornette

Saichev Alexander, I., Yannick Malevergne and Didier Sornette

ISBN 10: 3642029450 / ISBN 13: 9783642029455

Edité par Springer, 2009

A propos de cet article

Theory of Zipf's Law and Beyond (Lecture Notes in Economics and Mathematical Systems, Band 632) In deutscher Sprache. pages.

N° de réf. du vendeur BN542640

Détails bibliographiques

• Titre: Theory of Zipf's Law and Beyond (Lecture Notes in Economics and Mathematical Systems, Band 632) Saichev Alexander, I., Yannick Malevergne and Didier Sornette
• Éditeur: Springer
• Date de parution: 2009
• Langue: anglais
• ISBN à 10 chiffres: 3642029450
• ISBN à 13 chiffres: 9783642029455
• Reliure: Couverture souple
• Édition: 2009.
• État de l'article: gut
• Poids: 2000 grammes

A propos de ce titre

Synopsis

Zipf’s law is one of the few quantitative reproducible regularities found in e- nomics. It states that, for most countries, the size distributions of cities and of rms (with additional examples found in many other scienti c elds) are power laws with a speci c exponent: the number of cities and rms with a size greater thanS is inversely proportional toS. Most explanations start with Gibrat’s law of proportional growth but need to incorporate additional constraints and ingredients introducing deviations from it. Here, we present a general theoretical derivation of Zipf’s law, providing a synthesis and extension of previous approaches. First, we show that combining Gibrat’s law at all rm levels with random processes of rm’s births and deaths yield Zipf’s law under a “balance” condition between a rm’s growth and death rate. We nd that Gibrat’s law of proportionate growth does not need to be strictly satis ed. As long as the volatility of rms’ sizes increase asy- totically proportionally to the size of the rm and that the instantaneous growth rate increases not faster than the volatility, the distribution of rm sizes follows Zipf’s law. This suggests that the occurrence of very large rms in the distri- tion of rm sizes described by Zipf’s law is more a consequence of random growth than systematic returns: in particular, for large rms, volatility must dominate over the instantaneous growth rate.

Présentation de l'éditeur

This book presents a general theoretical derivation of Zipf's law, providing a synthesis and extension of previous approaches. It also offers a classification of the mechanisms responsible for deviations from Zipf's law.