dPowTS | R Documentation |
Evaluates the pdf for the symmetric power tempered stable distribution.
dPowTS(x, alpha, c = 1, ell = 1, mu = 0)
x |
Vector of points |
alpha |
Number in [0,2) |
c |
Parameter c >0 |
ell |
Parameter ell>0 |
mu |
Location parameter, any real number |
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).
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.
Michael Grabchak and Lijuan Cao
M. Grabchak (2016). Tempered Stable Distributions: Stochastic Models for Multiscale Processes. Springer, Cham.
x = (-10:10)/10 dPowTS(x,.5)
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