The characteristic function of the stable law

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Description

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

Usage

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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.

See Also

jacobianComplexCF

Examples

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# 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)

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