dTSS {TempStable}

Density function of the tempered stable subordinator (TSS) distribution

Description

The probability density function (PDF) of tempered stable subordinator distribution. It can be computed via the stable distribution (see details) using the stabledist package.

Usage

dTSS(x, alpha = NULL, delta = NULL, lambda = NULL, theta = NULL)

Arguments

x

A numeric vector of positive quantiles.

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.

f_{TSS}(y;\theta)=\mathrm{e}^{-\lambda y-\lambda^{\alpha}\delta\Gamma(-\alpha)}f_{S(\alpha,\delta)}(y),

where

f_{S(\alpha,\delta)}

is the density of the stable subordinator.

Value

As x is a numeric vector, the return value is also a numeric vector of probability densities.

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

Examples

x <- seq(0,15,0.25)
y <- dTSS(x,0.5,1,0.3)
plot(x,y)