jacobianComplexCF: Jacobian of the characteristic function of stable laws

In StableEstim: Estimate the Four Parameters of Stable Laws using Different Methods

Jacobian of the characteristic function of stable laws

Description

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

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.

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)

StableEstim documentation built on Aug. 7, 2022, 5:17 p.m.