| charTSS {TempStable} | R Documentation |
Characteristic function of the tempered stable subordinator
Description
Theoretical characteristic function (CF) of the distribution of the tempered stable subordinator. See Kawai & Masuda (2011) for details.
Usage
charTSS(t, alpha = NULL, delta = NULL, lambda = NULL, theta = NULL)
Arguments
t |
A vector of real numbers where the CF is evaluated. |
alpha |
Stability parameter. A real number between 0 and 1. |
delta |
Scale parameter. A real number > 0. |
lambda |
Tempering parameter. A real number > 0. |
theta |
Parameters stacked as a vector. |
Details
theta denotes the parameter vector (alpha, delta, lambda).
Either provide the parameters alpha, delta, lambda
individually OR provide theta.
\varphi_{TSS}(t;\theta):=E_{\theta}\left[
\mathrm{e}^{\mathrm{i}tY}\right]= \exp\left(\delta\Gamma(-\alpha)
\left((\lambda-\mathrm{i}t)^{\alpha}-\lambda^{\alpha}\right)\right)
Value
The CF of the tempered stable subordinator distribution.
References
Massing, T. (2023), 'Parametric Estimation of Tempered Stable Laws'
Kawai, R. & Masuda, H. (2011), 'On simulation of tempered stable random variates' doi:10.1016/j.cam.2010.12.014
Kuechler, U. & Tappe, S. (2013), 'Tempered stable distributions and processes' doi:10.1016/j.spa.2013.06.012
Examples
x <- seq(-10,10,0.25)
y <- charTSS(x,0.5,1,1)