pCTS: Cumulative probability function of the classic tempered stable (CTS) distribution

Description

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

Usage

pCTS(
  q,
  alpha = NULL,
  deltap = NULL,
  deltam = NULL,
  lambdap = NULL,
  lambdam = NULL,
  mu = NULL,
  theta = NULL,
  a = -40,
  b = 40,
  nf = 2^13,
  ...
)

Value

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

Arguments

q: A numeric vector of quantiles.
alpha: 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.
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 (alpha, deltap, deltam, lambdap, lambdam, mu). Either provide the parameters individually OR provide theta. The function integrates the PDF numerically with integrate().

Examples

Run this code

# \donttest{
x <- seq(-5,5,0.25)
y <- pCTS(x,0.5,1,1,1,1,1)
plot(x,y)
# }