IGParametersEstim: Estimate parameters of stable laws by Kogon and McCulloch methods
Description
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, ...)
Value
a vector of length 4 containing the estimates of the 4 parameters.
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 \(\beta\).
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.