Parameter Estimation for Symmetric Stable Distribution

A procedure is presented which is both direct and computationally feasible for the estimation of the parameters of the symmetric stable family. The most appealing property of the symmetric stable family is its invariance under convolution.The procedure presented uses a linearization of the sample characteristic function, the only aspect which is explicitly known for this distribution. All 3 parameters describing location, scale, and tail length are estimated simultaneously. The procedure uses Fama and Roll's estimates of location and scale for the initial standardization of data. Jackknifing procedures provide measures of standard errors. Jackknifing involves computing the estimators for all data and, after dividing the data into groups, repeating the computing of the estimators for each of the reduced bodies of data obtained by leaving out just one of the groups.