charTSS: Characteristic function of the tempered stable subordinator

In TempStable: A Collection of Methods to Estimate Parameters of Different Tempered Stable Distributions

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' \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.cam.2010.12.014")}

Kuechler, U. & Tappe, S. (2013), 'Tempered stable distributions and processes' \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.spa.2013.06.012")}

Examples

x <- seq(-10,10,0.25)
y <- charTSS(x,0.5,1,1)

TempStable documentation built on Oct. 24, 2023, 5:06 p.m.