| rTrunGamma {SubTS} | R Documentation |
Simulation from the truncated gamma distribution
Description
Simulates from the truncated gamma distribution.
Usage
rTrunGamma(n, t, mu, b = 1, step = 1)
Arguments
n |
Number of observations. |
t |
Parameter > 0. |
mu |
Parameter > 0. |
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 gamma distribution. This distribution has Laplace transform
L(z) = exp( t int_0^b (e^(-xz)-1) x^(-1)e^(-mu*x) dx), z>0
and Levy measure
M(dx) = t x^(-1) e^(-mu*x) 1(0<x<b) dx.
The simulation is performed by applying rejection sampling (Algorithm 4.4 in Dassios, Qu, Lim (2020)) to the generalized Dickman distribution. We simulate from the latter using Algorithm 3.1 in Dassios, Qu, Lim (2019).
Value
Returns a vector of n random numbers.
Author(s)
Michael Grabchak and Lijuan Cao
References
A. Dassios, Y. Qu, J.W. Lim (2019). Exact simulation of generalised Vervaat perpetuities. Journal of Applied Probability, 56(1):57-75.
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
rTrunGamma(10, 2, 1)