pGTS {TempStable}

Cumulative probability function of the generalized classical tempered stable (GTS) distribution

Description

The cumulative probability distribution function (CDF) of the generalized classical tempered stable distribution.

Usage

pGTS(
  q,
  alphap = NULL,
  alpham = NULL,
  deltap = NULL,
  deltam = NULL,
  lambdap = NULL,
  lambdam = NULL,
  mu = NULL,
  theta = NULL,
  dens_method = "FFT",
  a = -40,
  b = 40,
  nf = 2048,
  ...
)

Arguments

q

A numeric vector of quantiles.

alphap, alpham

Stability parameter. A real number between 0 and 2.

deltap

Scale parameter for the right tail. A real number > 0.

deltam

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

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.

...

Possibility to modify stats::integrate().

Details

theta denotes the parameter vector (alphap, alpham, deltap, deltam, lambdap, lambdam, 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 dGTS() density-function.

Examples

x <- seq(-1,1,1)
y <- pGTS(x,0.5,1.5,1,1,1,1,1)