ComputeFirstRootRealeCF: First root of the empirical characteristic function

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

First root of the empirical characteristic function

Description

Computes the first root of the real part of the empirical characteristic function.

Usage

ComputeFirstRootRealeCF(x, ..., tol = 0.001, maxIter = 100,
                        lowerBand = 1e-04, upperBand = 30)

Arguments

x	data used to perform the estimation: vector of length n.
...	other arguments to pass to the optimisation function.
tol	tolerance to accept the solution; default = 1e-3.
maxIter	maximum number of iteration in the Welsh algorithm; default = 100.
lowerBand	lower band of the domain where the graphical seach is performed; default = 1e-4.
upperBand	Lower band of the domain where the graphical seach is performed; default = 30.

Details

The Welsh algorithm is first applied. If it fails to provide a satisfactory value (< tol), a graphical/ numerical approach is used. We first plot the real part of the eCF vs t in order to determine the first zero directly and use it as the initial guess of a numerical minimisation routine.

Value

numeric: first zero of the real part of the eCF.

References

\insertRef

welsh1986implementingStableEstim

See Also

ComplexCF

Examples

set.seed(345)
x <- rstable(500, 1.5, 0.5)
ComputeFirstRootRealeCF(x)

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