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Tail Behavior, Modes and Other Characteristics of Stable Distributions (1999)
| Venue: | Extremes |
| Citations: | 11 - 2 self |
BibTeX
@ARTICLE{Fofack99tailbehavior,,
author = {Hippolyte Fofack and John P. Nolan},
title = {Tail Behavior, Modes and Other Characteristics of Stable Distributions},
journal = {Extremes},
year = {1999},
volume = {2},
pages = {39--58}
}
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Abstract
Stable distributions have heavy tails that are asymptotically Paretian. Accurate computations of stable densities and distribution functions are used to analyze when the Paretian tail actually appears. Implications for estimation procedures are discussed. In addition to numerically locating the mode of a general stable distribution, analytic and numeric results are given for the mode. Extensive tables of stable percentiles have been computed; aspects of these tables and the appropriateness of infinite variance stable models are discussed. Abbreviated title: Stable tails and modes 1 Introduction The Paretian tail behavior of stable distributions is the basis for their use as models when heavy tails are observed. The asymptotic behavior is also used to estimate the index of stability ff. However, little is actually known about the point at which this asymptotic behavior becomes accurate. Understanding when the approximation is accurate is also of interest for numerical purposes, where t...
Keyphrases
stable distribution tail behavior heavy tail extensive table numerical purpose asymptotic behavior becomes general stable distribution stable density paretian tail behavior paretian tail abbreviated title infinite variance stable model estimation procedure accurate computation numeric result stable tail stable percentile asymptotic behavior distribution function stability ff
