rPGamma: Simulation from p-gamma distributions.

In SubTS: Positive Tempered Stable Distributions and Related Subordinators

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)

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