This comprehensive text gives an interesting and useful blend of
the mathematical, probabilistic and statistical tools used in
heavy-tail analysis. Heavy tails are characteristic of many
phenomena where the probability of a single huge value impacts
heavily. Record-breaking insurance losses, financial-log returns,
files sizes stored on a server, transmission rates of files are all
examples of heavy-tailed phenomena.
Key features:
* Unique text devoted to heavy-tails
* Emphasizes both probability modeling and statistical methods
for fitting models. Most treatments focus on one or the other but
not both
* Presents broad applicability of heavy-tails to the fields of
data networks, finance (e.g., value-at- risk), insurance, and
hydrology
* Clear, efficient and coherent exposition, balancing theory and
actual data to show the applicability and limitations of certain
methods
* Examines in detail the mathematical properties of the
methodologies as well as their implementation in Splus or R
statistical languages
* Exposition driven by numerous examples and exercises
Prerequisites for the reader include a prior course in
stochastic processes and probability, some statistical background,
some familiarity with time series analysis, and ability to use (or
at least to learn) a statistics package such as R or Splus. This
work will serve second-year graduate students and researchers in
the areas of applied mathematics, statistics, operations research,
electrical engineering, and economics.
General
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