rKRTS {TempStable}

Function to generate random variates of KRTS distribution.

Description

Generates n random numbers distributed according to the Kim-Rachev tempered stable (KRTS) distribution.

Usage

rKRTS(
  n,
  alpha = NULL,
  kp = NULL,
  km = NULL,
  rp = NULL,
  rm = NULL,
  pp = NULL,
  pm = NULL,
  mu = NULL,
  theta = NULL,
  methodR = "SR",
  k = 10000
)

Arguments

n

sample size (integer).

alpha

Stability parameter. A real number between 0 and 2.

kp, km, rp, rm

Parameter of KR-distribution. A real number >0.

pp, pm

Parameter of KR-distribution. A real number >-alpha.

mu

A location parameter, any real number.

theta

Parameters stacked as a vector.

methodR

A String. Only "SR" is available here.

k

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

Details

theta denotes the parameter vector (alpha, kp, km, rp, rm, pp. pm, mu). Either provide the parameters individually OR provide theta. "SR" stands for a truncated infinite shot noise series representation. Currently, this method is the only implemented to generate random variates. The series representation is given by Bianchi et a. (2010).

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.

For more details, see references.

Value

Generates n random numbers of the KRTS distribution.

References

Bianchi, M. L.; Rachev, S. T.; Kim, Y. S. & Fabozzi, F. J. (2010), 'Tempered stable distributions and processes in finance: Numerical analysis' doi:10.1007/978-88-470-1481-7

Examples

rKRTS(1,0.5,1,1,1,1,1,1,0,NULL,"SR")