  Stable distribution is one of the attractive models that well describes
fat-tail behaviors and scaling phenomena in various scientific fields. The
approach based upon the method of moments yields a simple procedure for
estimating stable law parameters with the requirement of using momental points
for the characteristic function, but the selection of points is only poorly
explained and has not been elaborated. We propose a new characteristic
function-based approach by introducing a technique of selecting plausible
points, which could bring the method of moments available for practical use.
Our method outperforms other state-of-art methods that exhibit a closed-form
expression of all four parameters of stable laws. Finally, the applicability of
the method is illustrated by using several data of financial assets. Numerical
results reveal that our approach is advantageous when modeling empirical data
with stable distributions.
