Articles | Volume 24, issue 4
Research article
06 Dec 2017
Research article |  | 06 Dec 2017

Optimal heavy tail estimation – Part 1: Order selection

Manfred Mudelsee and Miguel A. Bermejo

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Subject: Time series, machine learning, networks, stochastic processes, extreme events | Topic: Climate, atmosphere, ocean, hydrology, cryosphere, biosphere
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Cited articles

Anderson, P. L. and Meerschaert, M. M.: Modeling river flows with heavy tails, Water Resour. Res., 34, 2271–2280, 1998.
Barabási, A.-L.: The origin of bursts and heavy tails in human dynamics, Nature, 435, 207–211, 2005.
Cronin, T. M.: Paleoclimates: Understanding Climate Change Past and Present. Columbia University Press, New York, 441 p., 2010.
Danielsson, J., de Haan, L., Peng, L., and de Vries, C. G.: Using a bootstrap method to choose the sample fraction in tail index estimation, J. Multivar. Anal., 76, 226–248, 2001.
D'Arrigo, R., Abram, N., Ummenhofer, C., Palmer, J., and Mudelsee, M.: Reconstructed streamflow for Citarum river, Java, Indonesia: Linkages to tropical climate dynamics, Clim. Dynam., 36, 451–462, 2011.
Short summary
Risk analysis of extremes has high socioeconomic relevance. Of crucial interest is the tail probability, P, of the distribution of a variable, which is the chance of observing a value equal to or greater than a certain threshold value, x. Many variables in geophysical systems (e.g. climate) show heavy tail behaviour, where P may be rather large. In particular, P decreases with x as a power law that is described by a parameter, α. We present an improved method to estimate α on data.