dorsal/arxiv
View SchemaPower-law distributions in economics: a nonextensive statistical approach
| Authors | Silvio M. Duarte Queiros, Celia Anteneodo, Constantino Tsallis |
|---|---|
| Categories | |
| ArXiv ID | physics/0503024 |
| URL | https://arxiv.org/abs/physics/0503024 |
| DOI | 10.1117/12.619469 |
| Journal | Power-law distributions in economics: a nonextensive statistical approach; Noise and Fluctuations in Econophysics and Finance, eds. D. Abbot, J.-P. Bouchaud, X. Gabaix and J.L. McCauley, Proc. of SPIE 5848, 151 (SPIE, Bellingham, WA, 2005) |
Abstract
The cornerstone of Boltzmann-Gibbs ($BG$) statistical mechanics is the Boltzmann-Gibbs-Jaynes-Shannon entropy $S_{BG} \equiv -k\int dx f(x)\ln f(x)$, where $k$ is a positive constant and $f(x)$ a probability density function. This theory has exibited, along more than one century, great success in the treatment of systems where short spatio/temporal correlations dominate. There are, however, anomalous natural and artificial systems that violate the basic requirements for its applicability. Different physical entropies, other than the standard one, appear to be necessary in order to satisfactorily deal with such anomalies. One of such entropies is $S_q \equiv k (1-\int dx [f(x)]^q)/(1-q)$ (with $S_1=S_{BG}$), where the entropic index $q$ is a real parameter. It has been proposed as the basis for a generalization, referred to as {\it nonextensive statistical mechanics}, of the $BG$ theory. $S_q$ shares with $S_{BG}$ four remarkable properties, namely {\it concavity} ($\forall q>0$), {\it Lesche-stability} ($\forall q>0$), {\it finiteness of the entropy production per unit time} ($q \in \Re$), and {\it additivity} (for at least a compact support of $q$ including $q=1$). The simultaneous validity of these properties suggests that $S_q$ is appropriate for bridging, at a macroscopic level, with classical thermodynamics itself. In the same natural way that exponential probability functions arise in the standard context,power-law tailed distributions, even with exponents {\it out} of the L\'evy range, arise in the nonextensive framework. In this review, we intend to show that many processes of interest in economy, for which fat-tailed probability functions are empirically observed, can be described in terms of the statistical mechanisms that underly the nonextensive theory.
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"abstract": "The cornerstone of Boltzmann-Gibbs ($BG$) statistical mechanics is the\nBoltzmann-Gibbs-Jaynes-Shannon entropy $S_{BG} \\equiv -k\\int dx f(x)\\ln f(x)$,\nwhere $k$ is a positive constant and $f(x)$ a probability density function.\nThis theory has exibited, along more than one century, great success in the\ntreatment of systems where short spatio/temporal correlations dominate. There\nare, however, anomalous natural and artificial systems that violate the basic\nrequirements for its applicability. Different physical entropies, other than\nthe standard one, appear to be necessary in order to satisfactorily deal with\nsuch anomalies. One of such entropies is $S_q \\equiv k (1-\\int dx\n[f(x)]^q)/(1-q)$ (with $S_1=S_{BG}$), where the entropic index $q$ is a real\nparameter. It has been proposed as the basis for a generalization, referred to\nas {\\it nonextensive statistical mechanics}, of the $BG$ theory. $S_q$ shares\nwith $S_{BG}$ four remarkable properties, namely {\\it concavity} ($\\forall\nq\u003e0$), {\\it Lesche-stability} ($\\forall q\u003e0$), {\\it finiteness of the entropy\nproduction per unit time} ($q \\in \\Re$), and {\\it additivity} (for at least a\ncompact support of $q$ including $q=1$). The simultaneous validity of these\nproperties suggests that $S_q$ is appropriate for bridging, at a macroscopic\nlevel, with classical thermodynamics itself. In the same natural way that\nexponential probability functions arise in the standard context,power-law\ntailed distributions, even with exponents {\\it out} of the L\\\u0027evy range, arise\nin the nonextensive framework. In this review, we intend to show that many\nprocesses of interest in economy, for which fat-tailed probability functions\nare empirically observed, can be described in terms of the statistical\nmechanisms that underly the nonextensive theory.",
"arxiv_id": "physics/0503024",
"authors": [
"Silvio M. Duarte Queiros",
"Celia Anteneodo",
"Constantino Tsallis"
],
"categories": [
"physics.soc-ph",
"physics.data-an",
"q-fin.ST"
],
"doi": "10.1117/12.619469",
"journal_ref": "Power-law distributions in economics: a nonextensive statistical\n approach; Noise and Fluctuations in Econophysics and Finance, eds. D. Abbot,\n J.-P. Bouchaud, X. Gabaix and J.L. McCauley, Proc. of SPIE 5848, 151 (SPIE,\n Bellingham, WA, 2005)",
"title": "Power-law distributions in economics: a nonextensive statistical approach",
"url": "https://arxiv.org/abs/physics/0503024"
},
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