A continuous representation of the family of stable law distributions


Cheng, R.C.H. and Liu, W.B. (1997) A continuous representation of the family of stable law distributions. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 59, (1), 137-145. (doi:10.1111/1467-9868.00059).

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Original Publication URL: http://dx.doi.org/10.1111/1467-9868.00059

Description/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
ISSNs: 1369-7412 (print)
Related URLs:
Subjects: Q Science > QA Mathematics
Divisions: University Structure - Pre August 2011 > School of Mathematics > Operational Research
ePrint ID: 29712
Date Deposited: 03 May 2007
Last Modified: 27 Mar 2014 18:18
Contact Email Address: R.C.H.Cheng@ukc.ac.uk
URI: http://eprints.soton.ac.uk/id/eprint/29712

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