Embedded distributions
From InterSciWiki
Power-law distributions may be embedded in stretched exponents or q-exponentials or other distributions. The terminology is that the power law may be necessary (for the tail) but not sufficient (for the larger distribution). Pisarenko's methods are used to estimate the convergent confidence limits of cutoffs as they converge with the power law. This is superior to the K-S approach used by Aaron Clauset.
- Yannick Malevergne is also in Didier Sornette's ETH Z group.
T. Maillart and D. Sornette Heavy-Tailed Distribution of Cyber-Risks. http://arxiv.org/PS_cache/arxiv/pdf/0803/0803.2256v1.pdf
--> Y. Malevergne, V.F. Pisarenko and D. Sornette, (2005): “Empirical distributions of stock returns: Exponential or power-law?”, Quantitative Finance 5, 379-401. (http://www.citebase.org/abstract?id=oai%3AarXiv.org%3Aphysics%2F0305089) ppt slides User:Douglas R. White has copy 02:46, 19 June 2008 (PDT)
Malevergne, Y., V.F. Pisarenko and D. Sornette, On the Power of Generalized Extreme Value (GEV) and Generalized Pareto Distribution (GPD) estimators for Empirical Distributions of Log-Returns, preprint (http://arXiv.org/abs/physics/0305089)
-->T. Maillart and D. Sornette, Heavy-tailed distribution of cyber-risks, submitted to Proc. Nat. Acad. Sci. USA (2008) (http://arxiv.org/abs/0803.2256) User:Douglas R. White has copy 02:46, 19 June 2008 (PDT)
V.F. Pisarenko and D.Sornette, New statistic for financial return distributions: power-law or exponential? Physica A (http://arXiv.org/abs/physics/0403075)
V. F. Pisarenko and D. Sornette, Statistical methods of parameter estimation for deterministically chaotic time series, Phys. Rev. E 69, 036122 (2004) (http://arXiv.org/abs/physics/0308059)
back to Short interviews with Didier Sornette
[edit] Other
D. Sornette, Probability Distributions in Complex Systems, Core article for the Encyclopedia of Complexity and System Science (Springer Science) (2007) (http://arxiv.org/abs/0707.2194)
