Robust Statistical Tests of Dragon-Kings beyond Power Law Distributions
| Autor: | Pisarenko, V. F., Sornette, D. |
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| Rok vydání: | 2011 |
| Předmět: | |
| Zdroj: | Eur. Phys. J. Special Topics 205, 95-115 (2012) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1140/epjst/e2012-01564-8 |
| Popis: | We ask the question whether it is possible to diagnose the existence of "Dragon-Kings" (DK), namely anomalous observations compared to a power law background distribution of event sizes. We present two new statistical tests, the U-test and the DK-test, aimed at identifying the existence of even a single anomalous event in the tail of the distribution of just a few tens of observations. The DK-test in particular is derived such that the p-value of its statistic is independent of the exponent characterizing the null hypothesis. We demonstrate how to apply these two tests on the distributions of cities and of agglomerations in a number of countries. We find the following evidence for Dragon-Kings: London in the distribution of city sizes of Great Britain; Moscow and St-Petersburg in the distribution of city sizes in the Russian Federation; and Paris in the distribution of agglomeration sizes in France. True negatives are also reported, for instance the absence of Dragon-Kings in the distribution of cities in Germany. Comment: 30 pages, 21 figures, 3 tables |
| Databáze: | arXiv |
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