Comparative study of stable parameter estimators and regression with stably distributed errors

Over the last several years there has been a growing interest in applying stable distributions to model real data. But their application had been difficult because all of the computations have to be done numerically. With the recent availability of more powerful computers, many different procedures have been developed to estimate the stable parameters, including the maximum likelihood estimation (MLE). In this work, we compare by simulation the different estimation procedures. We also develop a computer program to find MLE estimators for the regression coefficients when the errors are stably distributed, we discuss the properties of these estimators and test them through simulation.