A new method for estimating parameters of a skewed alpha-stable distribution

Estimating the parameters of a skewed α-stable distribution calls for estimation of four unknown parameters of the probability density function (PDF): the location parameter, the scale parameter, the characteristic exponent and the skewness parameter. We present cumulative distribution function (CDF) based estimators for either the location parameter, the skewness parameter, or the characteristic exponent. The estimators are simple, consistent and their asymptotic performance is analyzed. Of a particular interest is the new estimator for the skewness parameter which is given in a closed form, as a function of the other parameters. As such, it can be used for reducing the search dimension when joint parameter estimation of a skewed stable distribution is called for.