rNTS {TempStable}

Function to generate random variates of NTS distribution.

Description

Generates n random numbers distributed according of the normal tempered stable distribution.

Usage

rNTS(
  n,
  alpha = NULL,
  beta = NULL,
  delta = NULL,
  lambda = NULL,
  mu = NULL,
  theta = NULL,
  methodR = "TM",
  k = 10000
)

Arguments

n

sample size (integer).

alpha

A real number between 0 and 1.

beta

A gap holder.

delta

A real number > 0.

lambda

A real number > 0.

mu

A location parameter, any real number.

theta

A vector of all other arguments.

methodR

A String. Either "TM","AR" or "SR". "TM" by default.

k

integer: the number of replications, if methodR == "SR". 10000 by default.

Details

theta denotes the parameter vector (alpha, beta, delta, lambda, mu). Either provide the parameters individually OR provide theta. Works by a normal variance-mean mixture with a TSS distribution. Method parameter is for the method of simulating the TSS random variable, see the rTSS() function. "AR" stands for the Acceptance-Rejection Method and "SR" for a truncated infinite shot noise series representation. "TM" stands for Two Methods as two different methods are used depending on which will be faster. In this method the function copula::retstable() is called. "TM" is the standard method used. 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.

For more details, see references.

Value

Generates n random numbers.

References

Massing, T. (2023), 'Parametric Estimation of Tempered Stable Laws'

Kawai, R & Masuda, H (2011), 'On simulation of tempered stable random variates' doi:10.1016/j.cam.2010.12.014

Hofert, M (2011), 'Sampling Exponentially Tilted Stable Distributions' doi:10.1145/2043635.2043638

See Also

See also the rTSS() function. copula::retstable() as "TM" uses this function.

Examples

rNTS(100, 0.5, 1,1,1,1)
rNTS(10, 0.6, 0,1,1,0)
rNTS(10, 0.5, 1,1,1,1, NULL, "SR", 100)