pKRTS {TempStable}

Cumulative probability distribution function of the Kim-Rachev tempered stable (KRTS) distribution

Description

The cumulative probability distribution function (CDF) of the Kim-Rachev tempered stable distribution.

Usage

pKRTS(
  q,
  alpha = NULL,
  kp = NULL,
  km = NULL,
  rp = NULL,
  rm = NULL,
  pp = NULL,
  pm = NULL,
  mu = NULL,
  theta = NULL,
  dens_method = "FFT",
  a = -40,
  b = 40,
  nf = 2048,
  ...
)

Arguments

q

A vector of real numbers where the CF is evaluated.

alpha

Stability parameter. A real number between 0 and 2.

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. Currently, only "FFT" available.

a

Starting point of FFT, if dens_method == "FFT". -40 by default.

b

Ending point of FFT, if dens_method == "FFT". 40 by default.

nf

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

...

Possibility to modify stats::integrate().

Details

theta denotes the parameter vector (alpha, kp, km, rp, rm, pp. pm, mu)). Either provide the parameters individually OR provide theta. The function integrates the PDF numerically with integrate().

Value

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

See Also

See also the dKRTS() density-function.