Precise tabulation of the maximally-skewed stable distributions and densities

The cdf and pdf of the maximally skewed ( β = 1) stable distributions are tabulated to high precision, by means of Zolotarev's integral representation, for α = 0.50 (0.02) 2.00, at fractiles corresponding to p = 0.0001, 0.001, 0.005, 0.01 (0.01) 0.99, 0.995, 0.999, 0.9999. This tabulation is in...

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Bibliographic Details
Published in:Computational statistics & data analysis 1997-01, Vol.23 (3), p.307-320
Main Authors: Huston McCulloch, J., Panton, Don B.
Format: Article
Language:English
Subjects:
Maximally-skewed stable distributions
Numerical quadrature
Zolotarev integrals
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Summary:The cdf and pdf of the maximally skewed ( β = 1) stable distributions are tabulated to high precision, by means of Zolotarev's integral representation, for α = 0.50 (0.02) 2.00, at fractiles corresponding to p = 0.0001, 0.001, 0.005, 0.01 (0.01) 0.99, 0.995, 0.999, 0.9999. This tabulation is intended to be suitable for developing and calibrating a numerical approximation to these distributions. The probability at the tabulated fractiles is estimated to be accurate to within 4.1 × 10 −10. The densities have an absolute precision of 2.0 × 10 −13 and a relative precision of 1.6 × 10 −12. Zolotarev's correction of the discontinuity at α = 1 is graphically illustrated. The full tabulation, documented here, is available by anonymous FTP.
ISSN:0167-9473
1872-7352
DOI:10.1016/S0167-9473(96)00039-4