| rPGamma {SubTS} | R Documentation |
Simulation from p-gamma distributions.
Description
Simulates from p-gamma distributions. These are p-RDTS distributions with alpha=0.
Usage
rPGamma(n, t, mu, p, step = 1)
Arguments
n |
Number of observations. |
t |
Parameter >0. |
mu |
Parameter >0. |
p |
Parameter >1. |
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
Uses Theorem 1 in Grabchak (2021) to simulate from a p-Gamma distribution. This distribution has Laplace transform
L(z) = exp( t int_0^infty (e^(-xz)-1)e^(-(mu*x)^p) x^(-1) dx ), z>0
and Levy measure
M(dx) = t e^(-(mu*x)^p) x^(-1) 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
rPGamma(20, 2, 2, 2)