# CF: The characteristic function of the stable law In StableEstim: Estimate the Four Parameters of Stable Laws using Different Methods

## Description

Theoretical characteristic function (CF) of stable law under parametrisation ‘S0’ or ‘S1’. See Nolan (2013) for more details.

## Usage

 `1` ```ComplexCF(t, theta, pm = 0) ```

## Arguments

 `t` Vector of (real) numbers where the CF is evaluated ; numeric `theta` Vector of parameters of the stable law; vector of length 4. `pm` Parametrisation, an integer (0 or 1); default: `pm=0`( the Nolan ‘S0’ parametrisation).

## Details

For more details about the different parametrisation of the CF, see Nolan(2013).

## Value

Vector of complex numbers with dimension `length(t)`.

## References

Nolan JP (2013). Stable Distributions - Models for Heavy Tailed Data. Birkhauser, Boston. In progress, Chapter 1 online at academic2.american.edu/\\$sim\\$jpnolan.

`jacobianComplexCF`
 ```1 2 3 4 5 6 7 8``` ```# define the parameters nt <- 10 t <- seq(0.1,3,length.out=nt) theta <- c(1.5,0.5,1,0) pm <- 0 # Compute the characteristic function CF <- ComplexCF(t=t,theta=theta,pm=pm) ```