pCTS {TempStable}

Cumulative probability function of the classical tempered stable (CTS) distribution

Description

The cumulative probability distribution function (CDF) of the classical 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,
  ...
)

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().

Value

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

See Also

See also the dCTS() density-function.

Examples

x <- seq(-5,5,0.25)
y <- pCTS(x,0.5,1,1,1,1,1)
plot(x,y)