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 behavioural 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 paper, 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 Kiel Institute for the World Economy in its series Kiel Working Papers with number 1648.
Length: 10 pages
Date of creation: Sep 2010
Date of revision:
Power law; estimation; 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).
- Alfarano, Simone & Lux, Thomas, 2010. "Extreme Value Theory as a Theoretical Background for Power Law Behavior," MPRA Paper 24718, University Library of Munich, Germany.
- C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
- C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
- C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
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- 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.
- 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.
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