On the Skewness Parameter Estimation for Stable Distributions

#### S.M. Hosseini, J. Kabudian, S. Nadarajah, M. Teimouri

2015, v.21, №2, 369-380

ABSTRACT

The alpha-stable distributions have been extensively used as theoretical models for data.
In this note, we propose three new estimators for the skewness parameter of stable distributions.
Of these, the first and second estimators are introduced for $S1$ parameterization and
the third one for $S0$ parameterization.
Determining the sign of the skewness parameter is one of the important advantages of
the first estimator which is in fact a modification of the logarithmic moment approach.
Having consistency, asymptotic unbiasedness, closed form formulas and less computational complexity are some of the
major advantages of all of the proposed estimators.

Keywords: Pareto distribution; skewness parameter; stable distribution