A continuous representation of the family of stable law distributions

Cheng, Russell C.H., Liu, Wenbin (1997) A continuous representation of the family of stable law distributions. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 59 (1). pp. 137-145. ISSN 1369-7412. (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

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Abstract

Conventional parametric representations of stable law distributions do not allow all members of the family to be obtained as continuous limits of the parameters. Model building (or simulation) using such representations will be numerically unstable near such limits in consequence. Existing tables are not satisfactory near such limits as interpolation cannot be carried out. We show that these difficulties are overcome by using a new shifted Cartesian representation which characterizes the entire stable law family in a completely continuous way. Standardization is still possible with this representation so that tabulation, using just two bounded parameters, can be carried out. Its use is illustrated in a non-regular threshold estimation problem involving stable distributions which are discontinuous limits in conventional representations.

Item Type: Article
Uncontrolled keywords: Embedded models, Parameter estimation, Stable distributions, Tabulation
Subjects: Q Science > QA Mathematics (inc Computing science) > QA276 Mathematical statistics
Divisions: Faculties > Social Sciences > Kent Business School > Management Science
Depositing User: Steve Wenbin Liu
Date Deposited: 27 Nov 2013 09:36 UTC
Last Modified: 29 May 2019 11:28 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/36846 (The current URI for this page, for reference purposes)
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