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Mathematics - Probability Theory and Stochastic Processes | An Introduction to Heavy-Tailed and Subexponential Distributions

An Introduction to Heavy-Tailed and Subexponential Distributions

Foss, Sergey, Korshunov, Dmitry, Zachary, Stan

2011, IX, 123p. 1 illus..


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  • Provides a complete and comprehensive introduction to the theory of long
  • tailed and subexponential distributions
  • Discusses where the areas of applications currently stand -Includes preliminary mathematical material

Heavy-tailed probability distributions are an important component in the modeling of many stochastic systems. They are frequently used to accurately model inputs and outputs of computer and data networks and service facilities such as call centers. They are an essential for describing risk processes in finance and also for insurance premia pricing, and such distributions occur naturally in models of epidemiological spread. The class includes distributions with power law tails such as the Pareto, as well as the lognormal and certain Weibull distributions.

 This monograph defines the classes of long-tailed and subexponential distributions in one dimension and provides a complete and comprehensive description of their properties. New results are presented in a simple, coherent and systematic way. This leads to a comprehensive exposition of tail properties of sums of independent random variables whose distributions belong to the long-tailed and subexponential class.

The book includes a discussion of and references to contemporary areas of applications and also contains preliminary mathematical material which makes the book self contained. Modelers in the fields of finance, insurance, network science and environmental studies will find this book to be an essential reference.

Content Level » Graduate

Keywords » environmental modeling - financial modeling - lognormal distribution - long-tailed distribution - pareto distribution

Related subjects » Business, Economics & Finance - Complexity - Probability Theory and Stochastic Processes

Table of contents 

Preface.- Introduction.- Heavy- and long-tailed distributions.- Subexponential distributions.- Densities and local probabilities.- Maximum of random walks.- References.- Index

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