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Modeling Extreme Events Using Heavy-Tailed Distributions

  • Mathukumalli Vidyasagar

Abstract

Typically, in constructing a model for a random variable, one utilizes available samples to construct an empirical distribution function, which can then be used to estimate the probability that the random variable would exceed a prespecified threshold. However, in modeling extreme events, the threshold is often in excess of the largest sampled value observed thus far. In such cases, the use of empirical distributions would lead to the absurd conclusion that the random variable would never exceed the threshold. Therefore it becomes imperative to fit the observed samples with some appropriate distribution. For reasons explained in the paper, it is desirable to use the so-called stable distributions to fit the set of samples. In most cases, stable distributions are heavy-tailed, in that they do not have finite variance (and may not even have finite mean). However, they often do a very good job of fitting the data. This is illustrated in this paper via examples from various application areas such as finance and weather.

Keywords

Extreme Event Central Limit Theorem Empirical Distribution Stable Distribution Normal Random Variable 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

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  2. Nagaev AV (1969) Integral limit theorems taking large deviations into account when Cramér’s condition does not hold. Theory Probab Appl 14(1):51–67CrossRefMathSciNetGoogle Scholar
  3. Nagaev SN (1979) Large deviations of sums of independent random variables. Ann Probab 7(5):745–789CrossRefMathSciNetMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.The University of Texas at DallasRichardsonUSA
  2. 2.Indian Institute of Technology HyderabadKandi, MedakIndia

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