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 ar...

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Bibliographic Details
Published in:Journal of the Royal Statistical Society. Series B, Methodological Methodological, 1997, Vol.59 (1), p.137-145
Main Authors: Cheng, R. C. H., Liu, W. B.
Format: Article
Language:English
Subjects:
Cartesianism
Cauchy Lorentz distribution
Confidence interval
Cumulative distribution functions
Distribution
Distribution theory
Economic models
Eigenfunctions
embedded models
Exact sciences and technology
Family law
Interpolation
Kernel functions
Mathematics
parameter estimation
Parametric inference
Probability and statistics
Random variables
Sciences and techniques of general use
stable distributions
Statistical methods
Statistics
tabulation
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Summary: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.
ISSN:1369-7412
0035-9246
1467-9868
DOI:10.1111/1467-9868.00059