rTrunTS: Simulation from the truncated tempered stable distribution.

In SubTS: Positive Tempered Stable Distributions and Related Subordinators

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)

SubTS documentation built on March 7, 2023, 7:19 p.m.