Simulates from p-rapidly decreasing tempered stable (p-RDTS) distributions.
Usage
rPRDTS(n, t, mu, alpha, p, step = 1)
Value
Returns a vector of n random numbers.
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).
Author
Michael Grabchak and Lijuan Cao
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.
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.