rCTSP: Simulation of Fully Right Skewed CTS Distributions
Description
Simulates from fully right skewed classical tempered stable (CTS) distributions in both the finite and infinite variation cases. When alpha=0 this is the gamma distribution.
Usage
rCTSP(n, alpha, c, ell, epsilon = 0.5, p = 0.5)
Value
Returns a vector of n random numbers.
Arguments
n
Number of observations.
alpha
Parameter in [0,2).
c
Parameter >0.
ell
Tempering parameter >0.
epsilon
Tuning parameter in (0,1). Only for alpha>=1.
p
Tuning parameter in (0,1). Only for alpha>=1.
Author
Michael Grabchak and Lijuan Cao
Details
Simulates a fully right skewed CTS distribution. The distribution has Laplace transform
L(z) = exp( c int_0^infty (e^(-xz)-1)e^(-x/ell) x^(-1-alpha) dx), z>0
and Levy measure
M(dx) = c e^(-x/ell) x^(-1-alpha) 1(x>0)dx.
References
M. Grabchak (2016). Tempered Stable Distributions: Stochastic Models for Multiscale Processes. Springer, Cham.
M. Grabchak (2026). Exact Simulation from Tempered Stable Distributions with Infinite Variation (alpha>=1). <doi 10.48550/arXiv.2604.17732>.