Estimate parameters of stable laws by Kogon and McCulloch methods

Kogon regression method is used together with the McCulloch quantile method to provide initial estimates of parameters of stable distributions.

Usage

IGParametersEstim(x, pm = 0, ...)

Arguments

x: data used to perform the estimation: vector of length n.
pm: parametrisation, an integer (0 or 1); default: pm = 0 (Nolan's ‘S0’ parametrisation).
...: other arguments. Currently not used.

Details

The parameters \(\gamma\) and \(\delta\) are estimated using the McCulloch(1986) quantile method from fBasics. The data is rescaled using those estimates and used to perform the Kogon regression method to estimate \(\alpha\) and \(\beta\).

Value

a vector of length 4 containing the estimates of the 4 parameters.

References

Kogon SM and Williams DB (1998). “Characteristic function based estimation of stable distribution parameters.” A practical guide to heavy tailed data, pp. 311–335. McCulloch JH (1986). “Simple consistent estimators of stable distribution parameters.” Communications in Statistics-Simulation and Computation, 15(4), pp. 1109–1136.

Examples

x <- rstable(200, 1.2, 0.5, 1, 0, pm = 0)
IGParametersEstim(x, pm = 0)
#>     alpha      beta     gamma     delta 
#> 1.1843062 0.5841752 0.9112995 0.0107126