dNTS {TempStable}

Density function of the normal tempered stable (NTS) distribution

Description

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

Usage

dNTS(
  x,
  alpha = NULL,
  beta = NULL,
  delta = NULL,
  lambda = NULL,
  mu = NULL,
  theta = NULL,
  dens_method = "FFT",
  a = -20,
  b = 20,
  nf = 2048
)

Arguments

x

A numeric vector of quantile.

alpha

A real number between 0 and 1.

beta

Any real number.

delta

A real number > 0.

lambda

A real number > 0.

mu

A location parameter, any real number.

theta

A vector of all other arguments.

dens_method

Currently, useless param, as it does nothing and FFT is always used.

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.

Details

theta denotes the parameter vector (alpha, beta, delta, lambda, mu). Either provide the parameters individually OR provide theta. Currently, the only method is FFT.

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'

Examples

x <- seq(0,15,0.25)
y <- dNTS(x,0.8,1,1,1,1)
plot(x,y)