pMTS {TempStable}

Cumulative probability function of the modified tempered stable (MTS) distribution

Description

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

Usage

pMTS(
  q,
  alpha = NULL,
  delta = NULL,
  lambdap = NULL,
  lambdam = 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.

delta

Scale parameter. A real number > 0.

lambdap, lambdam

Tempering parameter. 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 (alpha, delta, 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.