dTSS {TempStable} | R Documentation |
The probability density function (PDF) of tempered stable subordinator distribution.
It can be computed via the stable distribution (see details)
using the stabledist
package.
dTSS(x, alpha = NULL, delta = NULL, lambda = NULL, theta = NULL)
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. |
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.
As x
is a numeric vector, the return value is also a numeric
vector of probability densities.
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
x <- seq(0,15,0.25)
y <- dTSS(x,0.5,1,0.3)
plot(x,y)