dSaS: PDF of Symmetric Stable Distribution

In SymTS: Symmetric Tempered Stable Distributions

PDF of Symmetric Stable Distribution

Description

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

Usage

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

Arguments

x	Vector of points.
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
dSaS(x,.5)

SymTS documentation built on Jan. 15, 2023, 1:06 a.m.