rRDTS {TempStable}

Function to generate random variates of RDTS distribution.

Description

Generates n random numbers distributed according to the rapidly decreasing tempered stable (CTS) distribution.

Usage

rRDTS(
  n,
  alpha = NULL,
  delta = NULL,
  lambdap = NULL,
  lambdam = NULL,
  mu = NULL,
  theta = NULL,
  methodR = "SR",
  k = 10000
)

Arguments

n

sample size (integer).

alpha

Stability parameter. A real number between 0 and 2.

delta

Scale parameter for the left tail. A real number > 0.

lambdap

Tempering parameter for the right tail. A real number > 0.

lambdam

Tempering parameter for the left tail. A real number > 0.

mu

A location parameter, any real number.

theta

Parameters stacked as a vector.

methodR

A String. Only "SR" works currently.

k

integer: the level of truncation, if methodR == "SR". 10000 by default.

Details

theta denotes the parameter vector (alpha, delta, lambdap, lambdam, mu). Either provide the parameters individually OR provide theta. "SR" stands for a truncated infinite shot noise series representation. Kim et al. (2010) showed how to simulate random variates with SR-method for the RDTS distribution. For more details, see references.

It is recommended to check the generated random numbers once for each distribution using the density function. If the random numbers are shifted, e.g. for the method "SR", it may be worthwhile to increase k.

Value

Generates n random numbers of the RDTS distribution.

References

Kim, Young Shi & Rachev, Svetlozar T. & Leonardo Bianchi, Michele & Fabozzi, Frank J. (2010), 'Tempered stable and tempered infinitely divisible GARCH models' doi:10.1016/j.jbankfin.2010.01.015

Examples

rCTS(10,0.5,1,1,1,1,1,NULL,"SR",10)
rCTS(10,0.5,1,1,1,1,1,NULL,"aAR")