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)
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.
Value
a matrix length(t) \(\times \) 4 of complex numbers.
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)