Chris Dance, Ercan kuruoglu
"Estimation of the parameters of skewed alpha-stable distributions" C Dance, E
Kuruoglu. Proceedings of Applications of Heavy-Tailed Distributions in Finance
and Engineering, 1999.
Stable distributions have received great interest over the last few years in
the signal processing community and have proved to be strong alternatives to
the Gaussian distribution. There have been several works in the literature
addressing the problem of estimating the parameters of stable distributions.
However, most of these works consider only the special case of symmetric stable
random variables. This is an important restriction though, since most real
life signals are skewed. Previous work on estimating the parameters of general
(possibly skewed) stable distributions has been limited. The existing
techniques are either computationally too expensive or their estimates have
high variances.

In this paper, we solve the general problem of stable parameter estimation
analytically. We introduce three novel classes of estimators for the
parameters of general stable distributions. These new classes of estimators
are based on formulas we have developed for the fractional and negative order
moments of skewed stable random variables. These are generalisations of
methods previously suggested for paramater estimation with symmetric stable

Of all known techniques for the general problem, only the characteristic
function technique and the methods we have suggested yield closed form
estimates for the parameters which may be efficiently computed. Simulation
results show that at least one of our new estimators has better performance
than the characteristic function technique over most of the parameter space.
Furthermore our techniques require substantially less computation.
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