Extreme Value Theory as a Theoretical Background for Power Law Behavior
AbstractPower law behavior has been recognized to be a pervasive feature of many phenomena in natural and social sciences. While immense research efforts have been devoted to the analysis of behavioral mechanisms responsible for the ubiquity of power-law scaling, the strong theoretical foundation of power laws as a very general type of limiting behavior of large realizations of stochastic processes is less well known. In this chapter, we briefly present some of the key results of extreme value theory, which provide a statistical justification for the emergence of power laws as limiting behavior for extreme fluctuations. The remarkable generality of the theory allows to abstract from the details of the system under investigation, and therefore allows its application in many diverse fields. Moreover, this theory offers new powerful techniques for the estimation of the Pareto index, detailed in the second part of this chapter.
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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 24718.
Date of creation: 2010
Date of revision:
Extreme Value Theory; Power Laws; Tail index;
Other versions of this item:
- Simone Alfarano & Thomas Lux, 2011. "Extreme Value Theory as a Theoretical Background for Power Law Behavior," Working Papers 2011/02, Economics Department, Universitat Jaume I, Castellón (Spain).
- Simone Alfarano & Thomas Lux, 2010. "Extreme Value Theory as a Theoretical Background for Power Law Behavior," Kiel Working Papers 1648, Kiel Institute for the World Economy.
- C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
- C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-09-11 (All new papers)
- NEP-ECM-2010-09-11 (Econometrics)
- NEP-HPE-2010-09-11 (History & Philosophy of Economics)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Drees, Holger & Kaufmann, Edgar, 1998. "Selecting the optimal sample fraction in univariate extreme value estimation," Stochastic Processes and their Applications, Elsevier, vol. 75(2), pages 149-172, July.
- Hall, Peter, 1990. "Using the bootstrap to estimate mean squared error and select smoothing parameter in nonparametric problems," Journal of Multivariate Analysis, Elsevier, vol. 32(2), pages 177-203, February.
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