  The class of $\alpha$-stable distributions received much interest for
modelling impulsive phenomena occur in engineering, economics, insurance, and
physics. The lack of non-analytical form for probability density function is
considered as the main obstacle to modelling data via the class of
$\alpha$-stable distributions. As the central member of this class, the Cauchy
distribution has received many applications in economics, seismology,
theoretical and applied physics. We derive estimators for the parameters of the
Cauchy and mixture of Cauchy distributions through the EM algorithm.
Performance of the EM algorithm is demonstrated through simulations and real
sets of data.
