1998/01/28 by J. Laherrère, Jean Laherrère, D. Sornette · 13 citations
Economics, Econometrics and Finance · Physics and Astronomy · #Complex Systems and Time Series Analysis #Statistical Mechanics and Entropy #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1007/s100510050276
published as Eur.Phys.J. B2 (1998) 525-539 · 17 pages, 16 sets of figures, in press in European Physical Journal B
arxiv created 1998/01/28 · crossref issued 1998/05/01 · crossref published 1998/05/01 · crossref published-print 1998/05/01 · openalex publication_date 1998/05/01 · crossref created 2002/08/25 · arxiv updated 2009/11/30 · crossref deposited 2019/05/29 · openalex created_date 2019/06/27 · crossref indexed 2026/07/15 · openalex updated_date 2026/07/28
To account quantitatively for many reported ``natural'' fat tail distributions in Nature and Economy, we propose the stretched exponential family as a complement to the often used power law distributions. It has many advantages, among which to be economical with only two adjustable parameters with clear physical interpretation. Furthermore, it derives from a simple and generic mechanism in terms of multiplicative processes. We show that stretched exponentials describe very well the distributions of radio and light emissions from galaxies, of US GOM OCS oilfield reserve sizes, of World, US and French agglomeration sizes, of country population sizes, of daily Forex US-Mark and Franc-Mark price variations, of Vostok temperature variations, of the Raup-Sepkoski's kill curve and of citations of the most cited physicists in the world. We also briefly discuss its potential for the distribution of earthquake sizes and fault displacements and earth temperature variations over the last 400 000 years. We suggest physical interpretations of the parameters and provide a short toolkit of the statistical properties of the stretched exponentials. We also provide a comparison with other distributions, such as the shifted linear fractal, the log-normal and the recently introduced parabolic fractal distributions.