pPowTS {SymTS}

PDF of PowTS Distribution

Description

Evaluates the cdf for the symmetric power tempered stable distribution.

Usage

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

Arguments

x

Vector of probabilities.

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).

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
pPowTS(x,.5)