However several approximations to the MLE do exist. E. F. Fama and R. Roll.
Parameter estimates for symmetric stable distributions .
So by estimating certain quantiles from the data it is possible to estimate stable parameters using the tables of quantiles for real stable distributions. E. Fama and R. Roll. Parameter estimates for symmetric stable distributions . In this section we briefly introduce these techniques and finish with a summary of their valid estimation ranges. However their technique was limited to symmetric distributions and suffered from a small asymptotic bias.