Regression-Type Estimation of the Parameters of Stable Laws

Abstract A regression-type method of estimating the four parameters of a stable distribution is presented. The estimators found are consistent and approximately unbiased for moderately large sample sizes. Their efficiencies, found through a simulation study, are greater than those of most other estimators for large portions of the parameter space. Moreover, the amount of computation involved is minimal and apparently less than that needed by the methods of Paulson, Holcomb, and Leitch (1975) and of maximum likelihood (DuMouchel 1971). Finally, this method is applied to stock price data from four corporations.