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Title: Density of near-extreme events
Authors: Sabhapandit, Sanjib
Majumdar, Satya N.
Keywords: probability theory
stochastic processes
fluctuation phenomena
random processes
time series analysis
Issue Date: Apr-2007
Publisher: American Physical Society
Citation: Physical Review E, 2007, Vol.98, p140201
Abstract: We provide a quantitative analysis of the phenomenon of crowding of near-extreme events by computing exactly the density of states (DOS) near the maximum of a set of independent and identically distributed random variables. We show that the mean DOS converges to three different limiting forms depending on whether the tail of the distribution of the random variables decays slower than pure exponential, faster than pure exponential, or as a pure exponential function. We argue that some of these results would remain valid even for certain correlated cases and verify it for power-law correlated stationary Gaussian sequences. Satisfactory agreement is found between the near-maximum crowding in the summer temperature reconstruction data of western Siberia and the theoretical prediction.
Description: Restricted Access. An open-access version is available at (one of the alternative locations)
ISSN: 1539-3755
1550-2376 (Online)
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Copyright: 2007 The American Physical Society
Appears in Collections:Research Papers (TP)

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