rCTSM: Simulation of Fully Left Skewed CTS Distributions

In SubTS: Tempered Stable Subordinators and Related Distributions

Simulation of Fully Left Skewed CTS Distributions

Description

Simulates from fully left skewed classical tempered stable (CTS) distributions in both the finite and infinite variation cases. When alpha=0 this is the negative of the gamma distribution.

Usage

rCTSM(n, alpha, c, ell, epsilon = 0.5, p = 0.5)

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.

Details

Simulates from a fully left skewed CTS distribution. The distribution has moment generating function

M(z) = exp( c int_(-infty)^0 (e^(xz)-1)e^(-x/ell) x^(-1-alpha) dx)

and Levy measure

M(dx) = c e^(-|x|/ell) |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 (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>.

Examples

rCTSM(20, 1.5, 1, 1)

SubTS documentation built on Sept. 14, 2026, 1:06 a.m.