The family of stable distributions represents an important generalization of the Gaussian family; stable random variables obey a generalized central limit theorem where the assumption of finite variance is replaced with one of power law decay in the tails. Possessing heavy tails, asymmetry, and infinite variance, non-Gaussian stable distributions can be suitable for inference in settings featuring impulsive, possibly skewed noise. A general lack of analytical form for the densities and distributions of stable laws has prompted research into computational methods of estimation. This report introduces stable distributions through a discussion of their basic properties and definitions in chapter 1. Chapter 2 surveys applications, and chapter 3 discusses a number of procedures for inference, with particular attention to time series models in the ARMA setting. Further details and an application can be found in the appendices. / text
| Identifer | oai:union.ndltd.org:UTEXAS/oai:repositories.lib.utexas.edu:2152/29165 |
| Date | 16 March 2015 |
| Creators | Ghaffari, Novin |
| Source Sets | University of Texas |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | application/pdf |
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