dRDTS {TempStable}

Density function of the rapidly decreasing tempered stable (CTS) distribution

Description

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

Usage

dRDTS(
  x,
  alpha = NULL,
  delta = NULL,
  lambdap = NULL,
  lambdam = NULL,
  mu = NULL,
  theta = NULL,
  dens_method = "FFT",
  a = -20,
  b = 20,
  nf = 256
)

Arguments

x

A numeric vector of quantiles.

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.

dens_method

Algorithm for numerical evaluation. Choose "FFT".

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. 256 by default.

Details

theta denotes the parameter vector (alpha, delta, lambdap, lambdam, mu). Either provide the parameters individually OR provide theta. Methods include only the the Fast Fourier Transform (FFT).

For examples, compare with dCTS().

Value

As x is a numeric vector, the return value is also a numeric vector of densities.

References

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