StableEstim (version 2.4)

jacobianComplexCF: Jacobian of the characteristic function of stable laws

Description

Numeric jacobian of the characteristic function (CF) as a function of the parameter \(\theta\) evaluated at a specific (vector) point t and a given value \(\theta\).

Usage

jacobianComplexCF(t, theta, pm = 0)

Value

a matrix length(t)

\(\times \) 4 of complex numbers.

Arguments

t

vector of (real) numbers where the jacobian of 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

The numerical derivation is obtained by a call to the function jacobian from package numDeriv. We have set up its arguments by default and the user is not given the option to modify them.

See Also

ComplexCF

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 jacobian of the characteristic function
jack_CF <- jacobianComplexCF(t = t, theta = theta, pm = pm)