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A continuous representation of the family of stable law distributions

Record type: Article

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.

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Citation

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), pp. 137-145. (doi:10.1111/1467-9868.00059).

More information

Published date: 1997
Organisations: Operational Research

Identifiers

Local EPrints ID: 29712
URI: http://eprints.soton.ac.uk/id/eprint/29712
ISSN: 1369-7412
PURE UUID: 8e4326fb-3e4e-4c48-a27e-e1782cc790b3

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Date deposited: 03 May 2007
Last modified: 17 Jul 2017 15:57

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Contributors

Author: R.C.H. Cheng
Author: W.B. Liu

University divisions


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