An iterative procedure for the estimation of the parameters of stable laws

Abstract

The sample characteristic function is used in an iterative procedure for estimating the parameters of a stable law. This method refines an earlier-developed two-step procedure which finds estimators of the characteristic exponent, a, skewness b, scale c, and location parameter 6 from non-weighted linear regressions. A number of simulation experiments with the new method show an improvement in terms of mean square error over the previous method in most cases. In particular, the improvement in estimating the parameter 3 for distributions which do not have both a close to two and 3 close to zero, and the improvement in estimating the parameters a and 6 when a is close to zero are substantial.

Keywords:

• Regression-type estimators
• sample characteristic function
• stable laws