dMTS {TempStable}

Density function of the modified tempered stable (MTS) distribution

Description

theta denotes the parameter vector (alpha, delta, lambdap, lambdam, mu). The probability density function (PDF) of the modified tempered stable distributions is not available in closed form. Relies on fast Fourier transform (FFT) applied to the characteristic function.

Usage

dMTS(
  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. 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. 256 by default.

Details

For examples, compare with dCTS().

Value

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