Compute the characteristic function of stable laws

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

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 (Nolan's ‘S0’ parametrisation).

Details

For more details about the different parametrisation of the CF, see Nolan(2012).

Value

vector of complex numbers with dimension length(t).

References

Nolan JP (2012). Stable Distributions - Models for Heavy Tailed Data. Birkhauser, Boston. In progress, Chapter 1 online at academic2.american.edu/\(\sim\)jpnolan.

See also

jacobianComplexCF

Examples

## 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)
CF
#>  [1] 0.968305811+0.033117936i 0.757986409+0.056143306i 0.525387123+0.026851945i
#>  [4] 0.332271933-0.005812349i 0.193104300-0.024061787i 0.102956859-0.027785107i
#>  [7] 0.049972446-0.023103095i 0.021746183-0.015850609i 0.008231545-0.009409216i
#> [10] 0.002521428-0.004930514i