dGTS {TempStable}

Density function of generalized classical tempered stable distribution

Description

The probability density function (PDF) of the generalized classical tempered stable (GTS) distributions is not available in closed form. Relies on fast Fourier transform (FFT) applied to the characteristic function.

Usage

dGTS(
  x,
  alphap = NULL,
  alpham = NULL,
  deltap = NULL,
  deltam = NULL,
  lambdap = NULL,
  lambdam = NULL,
  mu = NULL,
  theta = NULL,
  dens_method = "FFT",
  a = -20,
  b = 20,
  nf = 2048
)

Arguments

x

A numeric vector of positive quantiles.

alphap, alpham

Stability parameter. A real number between 0 and 2.

deltap, deltam

Scale parameter. A real number > 0.

lambdap, lambdam

Tempering parameter. A real number > 0.

mu

A location parameter, any real number.

theta

Parameters stacked as a vector.

dens_method

A method to get the density function. Here, only "FFT" is available.

a

Starting point of FFT, if dens_method == "FFT". -20 by default.

b

Ending point of FFT, if dens_method == "FFT". 20 by default.

nf

Pieces the transformation is divided in. Limited to power-of-two size. Default is 2048.

Value

As q is a numeric vector, the return value is also a numeric vector of probabilities.

Examples

x <- seq(-5,5,0.25)
y <- dGTS(x,0.3,0.2,1,1,1,1,0)