# McCulloch-Panton Skew-Stable Fractile Density Table

** McCulloch-Panton Skew-Stable Fractile Density Table (439 KB),**
as documented in J. Huston McCulloch and Don B. Panton,

"Precise Tabulation of the
Maximally-Skewed Stable
Distributions and Densities,"

* Computational Statistics and Data
Analysis * vol. 23 (Jan. 1997), pp. 307-320.

First column gives alpha. Second column gives cumulative
probability. Third column gives corresponding quantile
for beta = 1. Fourth column gives density at quantile.
The reader is also referred to
Geoff Robinson,
"Rapid Computations Concerning Log Maximally-Skewed Stable Distributions,
With Potential Use for Pricing Options and Evaluating Portfoio Risk,"
Sept. 2005, online at
http://www.cmis.csiro.au/geoff.robinson/combined.pdf. Robinson
confirms, using extended precision (16 byte) calculations, that the
probabilities and densities at the estimated fractiles tabulated in the
above file have absolute accuracies well
within 4.1e-10 and 2.0e-13, respectively, as claimed in the McCulloch
and Panton paper. However, he detected four instances in which
the relative density error exceeded the 1.6e-12 claimed by
McCulloch and Panton. The worst of these, for p = 0.9999 and alpha = 1.0,
was 2.6e-10. The latter value should therefore be used as an upper
bound on the relative density precisions in the above file, and
we are grateful to Robinson for correcting this overstatement
in our paper.

The source of our error probably lay in the fact that we were
only using standard double precision (8 byte) arithmetic, with the
result that rounding errors may have accumulated in excess
of the pure quadrature errors that we did attempt to quantify.

The following graphs are plotted from the data in the above tabulation.
"Zeta" = tan(pi*alpha/2)is a shift factor that induces continuity in
the plotted surface.

## Skew-Stable Densities

## Skew-Stable Distributions

Corrected precisions added 9/26/05.

Up to JHM homepage.