pSaS {SymTS}

CDF of Symmetric Stable Distribution

Description

Evaluates the cdf for the symmetric alpha stable distribution. For alpha=1 this is the Cauchy distribution.

Usage

pSaS(x, alpha, c = 1, mu = 0)

Arguments

x

Vector of probabilities.

alpha

Index of stability; Number in (0,2)

c

Scale parameter, c>0

mu

Location parameter, any real number

Details

The integration is preformed using the QAWF method in the GSL library for C. The characteristic function is

f(t) = e^(-c |t|^alpha) *e^(i*t*mu).

Author(s)

Michael Grabchak and Lijuan Cao

References

G. Samorodnitsky and M. Taqqu (1994). Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance. Chapman & Hall, Boca Raton.

Examples

x = (-10:10)/10
pSaS(x,.5)