A continuous representation of the family of stable law distributions
A continuous representation of the family of stable law distributions
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.
137-145
Cheng, R.C.H.
a4296b4e-7693-4e5f-b3d5-27b617bb9d67
Liu, W.B.
d3765562-2020-485e-9a1c-61ff5b1f3a90
1997
Cheng, R.C.H.
a4296b4e-7693-4e5f-b3d5-27b617bb9d67
Liu, W.B.
d3765562-2020-485e-9a1c-61ff5b1f3a90
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), .
(doi:10.1111/1467-9868.00059).
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.
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Published date: 1997
Organisations:
Operational Research
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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: 15 Mar 2024 07:34
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W.B. Liu
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