Precise tabulation of the maximally-skewed stable distributions and densities
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چکیده
The cdf and pdf of the maximally skewed (/~ = 1) stable distributions are tabulated to high precision, by means of Zolotarev's integral representation, for ct = 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~o. The densities have an absolute precision of 2.0 x 10-13 and a relative precision of 1.6 x 10-12. Zolotarev's correction of the discontinuity at ct = 1 is graphically illustrated. The full tabulation, documented here, is available by anonymous FTP.
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تاریخ انتشار 1997