| rPRDTS {SubTS} | R Documentation |
Simulation from p-RDTS distributions.
Description
Simulates from p-rapidly decreasing tempered stable (p-RDTS) distributions.
Usage
rPRDTS(n, t, mu, alpha, p, step = 1)
Arguments
n |
Number of observations. |
t |
Parameter >0. |
mu |
Parameter >0. |
alpha |
Parameter in (-infty,1) |
p |
Parameter >1 if 0<=alpha<1, >0 if alpha<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 a p-RDTS distribution. When alpha >=0, uses Theorem 1 in Grabchak (2021) and when alpha<0 uses the method in Section 4 of Grabchak (2021). This distribution has Laplace transform
L(z) = exp( t int_0^infty (e^(-xz)-1)e^(-(mu*x)^p) x^(-1-alpha) dx ), z>0
and Levy measure
M(dx) = t e^(-(mu*x)^p) x^(-1-alpha) 1(x>0)dx.
Value
Returns a vector of n random numbers.
Author(s)
Michael Grabchak and Lijuan Cao
References
M. Grabchak (2019). Rejection sampling for tempered Levy processes. Statistics and Computing, 29(3):549-558
M. Grabchak (2021). An exact method for simulating rapidly decreasing tempered stable distributions. Statistics and Probability Letters, 170: Article 109015.
M. Hofert (2011). Sampling exponentially tilted stable distributions. ACM Transactions on Modeling and Computer Simulation, 22(1), 3.
Examples
rPRDTS(20, 2, 1, .7, 2)
rPRDTS(20, 2, 1, 0, 2)
rPRDTS(20, 2, 1, -.7, 2)