TempStable (version 0.1.0)

charTSS: 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)

Value

The CF of the tempered stable subordinator distribution.

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. $$\varphi_{TSS}(t;\theta):=E_{\theta}\left[ \mathrm{e}^{\mathrm{i}tY}\right]= \exp\left(\delta\Gamma(-\alpha) \left((\lambda-\mathrm{i}t)^{\alpha}-\lambda^{\alpha}\right)\right)$$

References

Massing, T. (2023), 'Parametric Estimation of Tempered Stable Laws'

Kawai, R. & Masuda, H. (2011), 'On simulation of tempered stable random variates' tools:::Rd_expr_doi("10.1016/j.cam.2010.12.014")

Kuechler, U. & Tappe, S. (2013), 'Tempered stable distributions and processes' 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)