JSM 2005 - Toronto

Abstract #304395

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Activity Number: 330
Type: Contributed
Date/Time: Tuesday, August 9, 2005 : 2:00 PM to 3:50 PM
Sponsor: Business and Economics Statistics Section
Abstract - #304395
Title: Modeling Heavy-tailed Distributions
Author(s): Annapurna Ravi*+ and Ferry Butar Butar
Companies: Sam Houston State University and Sam Houston State University
Address: 555 Bowers Blvd, Huntsville, TX, 77340, United States
Keywords: Stable Distributions ; Heavy-tailed data ; Large datasets ; Financial applications
Abstract:

Heavy tailed distributions are encountered in numerous fields such as economics, finance, geophysics, and insurance. Stable distributions are one class of distributions used to model heavy-tailed data. Heavy-tailed data can be either symmetric or asymmetric. Stable distributions can be applied to either case equally. Many large datasets---such as datasets from satellites, natural calamities, and actuarial studies---exhibit heavy tails and skewness. Such datasets cannot be described properly by a Gaussian model, but can be described well by a stable distribution. This paper discusses various parameters of stable distributions and how heavy-tailed distributions are modeled using stable distributions. It compares stable distributions and Gaussian modeling and explores negative effects of a stable distribution not having a closed-form expression. Again, the computational methods of calculating the reliable stable density function depend on the size of the dataset, calculation time, required accuracy, and values of parameters. Application of the distribution to financial data, where there is a possibility for high and low volatile phases, concludes the paper.

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