The increasing interest in the application of geometric stable distributions has lead to a need for appropriate estimators. Building on recent procedures for estimating the Linnik distribution, this paper develops two estimators for the geometric stable distribution. Closed form expressions are provided for the signed and unsigned fractional moments of the distribution. The estimators are then derived using the methods of fractional lower order moments and that of logarithmic moments. Their performance is tested on simulated data, where the lower order estimators, in particular, are found to give efficient results over most of the parameter space.
Halvarsson, D. (2013). ”On the Estimation of Skewed Geometric Stable Distribution”. Ratio Working paper No. 216.