dKRTS {TempStable}

Density Function of the Kim-Rachev tempered stable distribution

Description

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

Usage

dKRTS(
  x,
  alpha = NULL,
  kp = NULL,
  km = NULL,
  rp = NULL,
  rm = NULL,
  pp = NULL,
  pm = NULL,
  mu = NULL,
  theta = NULL,
  dens_method = "FFT",
  a = -20,
  b = 20,
  nf = 256
)

Arguments

x

A numeric vector of positive quantiles.

alpha

Stability parameter. A real number between 0 and 1.

kp, km, rp, rm

Parameter of KR-distribution. A real number >0.

pp, pm

Parameter of KR-distribution. A real number >-alpha.

mu

A location parameter, any real number.

theta

Parameters stacked as a vector.

dens_method

Algorithm for numerical evaluation. Here you can only 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, kp, km, rp, rm, pp. pm, mu). Either provide the parameters individually OR provide theta.

For examples, compare with dCTS().

Value

The CF of the the Kim-Rachev tempered stable distribution.