dPowTS: PDF of PowTS Distribution

In SymTS: Symmetric Tempered Stable Distributions

PDF of PowTS Distribution

Description

Evaluates the pdf for the symmetric power tempered stable distribution.

Usage

dPowTS(x, alpha, c = 1, ell = 1, mu = 0)

Arguments

x	Vector of points
alpha	Number in [0,2)
c	Parameter c >0
ell	Parameter ell>0
mu	Location parameter, any real number

Details

The integration is preformed using the QAWF method in the GSL library for C. For this distribution the Rosinski measure R(dx) = c*(alpha+ell+1)*(alpha+ell)*(1+|x|)^(-2-alpha-ell)(dx).

Note

We do not allow for the case alpha=0 and c<=.5*(1+ell), as, in this case, the pdf is unbounded. This does not affect pPowTS, qPowTS, or rPowTS.

Author(s)

Michael Grabchak and Lijuan Cao

References

M. Grabchak (2016). Tempered Stable Distributions: Stochastic Models for Multiscale Processes. Springer, Cham.

Examples

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

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