  The class of $\alpha$-stable distributions with a wide range of applications
in economics, telecommunications, biology, applied, and theoretical physics.
This is due to the fact that it possesses both the skewness and heavy tails.
Since $\alpha$-stable distribution suffers from a closed-form expression for
density function, finding efficient estimators for its parameters has attracted
a great deal of attention in the literature. Here, we propose some EM algorithm
to estimate the maximum likelihood estimators of the parameters of
$\alpha$-stable distribution. The performance of the proposed EM algorithm is
demonstrated via comparison study in the presence of other well-known
competitors and analyzing three sets of real data.
