| rTrunTS {SubTS} | R Documentation |
Simulation from the truncated tempered stable distribution.
Description
Simulates from the truncated tempered stable distribution.
Usage
rTrunTS(n, t, mu, alpha, b = 1, step = 1)
Arguments
n |
Number of observations. |
t |
Parameter > 0. |
mu |
Parameter > 0. |
alpha |
Parameter in the open interval (0,1). |
b |
Parameter > 0. |
step |
Tuning parameter. The larger the step, the slower the rejection sampling, but the fewer the number of terms. See Hoefert (2011) or Section 4 in Grabchak (2019). |
Details
Simulates from the truncated stable distribution using Algorithm 4.3 in Dassios, Qu, and Lim (2020). This distribution has Laplace transform
L(z) = exp( t * (alpha/Gamma(1-alpha)) * int_0^b (e^(-xz)-1) x^(-1-alpha) e^(-mu*x) dx), z>0
and Levy measure
M(dx) = t * (alpha/Gamma(1-alpha)) * x^(-1-alpha) e^(-mu*x) 1(0<x<b) dx.
Here Gamma() is the gamma function.
Value
Returns a vector of n random numbers.
Author(s)
Michael Grabchak and Lijuan Cao
References
A. Dassios, Y. Qu, J.W. Lim (2020). Exact simulation of a truncated Levy subordinator. ACM Transactions on Modeling and Computer Simulation, 30(10), 17.
M. Grabchak (2019). Rejection sampling for tempered Levy processes. Statistics and Computing, 29(3):549-558
M. Hofert (2011). Sampling exponentially tilted stable distributions. ACM Transactions on Modeling and Computer Simulation, 22(1), 3.
Examples
rTrunTS(10, 2, 2, .6)