Simple consistent estimators of stable distribution parameters

Abstract

The four parameters of a stable distribution may be estimated consistently from five pre-determined sample quantiles with the aid of the accompanying tables, for a in the range [0.6, 2.0] and g in the range [-1, 1]. The problem of the discontinuity of the traditional location parameter in the asymmetrical cases as a passes unity is resolved. The proposed estimators of a and c are similar to those of Fama and Roll, except that the small asymptotic bias in their estimators has been eliminated, and their restrictions that a be no less than 1.0 and that the distribution be symmetrical have been relaxed. The proposed estimators can provide good initialization values for other more efficient, but computer-intensive, methods.