Theoretical characteristic function (CF) of the classical tempered stable distribution. See Kuechler & Tappe (2013) for details.
charCTS(
t,
alpha = NULL,
deltap = NULL,
deltam = NULL,
lambdap = NULL,
lambdam = NULL,
mu = NULL,
theta = NULL
)The CF of the tempered stable subordinator distribution.
A vector of real numbers where the CF is evaluated.
Stability parameter. A real number between 0 and 2.
Scale parameter for the right tail. A real number > 0.
Scale parameter for the left tail. A real number > 0.
Tempering parameter for the right tail. A real number > 0.
Tempering parameter for the left tail. A real number > 0.
A location parameter, any real number.
Parameters stacked as a vector.
theta denotes the parameter vector (alpha, deltap, deltam,
lambdap, lambdam, mu). Either provide the parameters individually OR
provide theta.
$$\varphi_{CTS}(t;\theta):=
E_{\theta}\left[
\mathrm{e}^{\mathrm{i}tX}\right]=
\exp\left(\mathrm{i}t\mu+\delta_+\Gamma(-\alpha)
\left((\lambda_+-\mathrm{i}t)^{\alpha}-\lambda_+^{\alpha}+
\mathrm{i}t\alpha\lambda_+^{\alpha-1}\right)\right.\\$$
$$\left. +\delta_-\Gamma(-\alpha)
\left((\lambda_-+\mathrm{i}t)^{\alpha}-\lambda_-^{\alpha}-\mathrm{i}t\alpha
\lambda_-^{\alpha-1}\right)
\right)$$
Massing, T. (2023), 'Parametric Estimation of Tempered Stable Laws'
Kuechler, U. & Tappe, S. (2013), 'Tempered stable distributions and processes' tools:::Rd_expr_doi("10.1016/j.spa.2013.06.012")
x <- seq(-10,10,0.25)
y <- charCTS(x,1.5,1,1,1,1,0)
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