  The class of $\alpha$-stable distributions is widely used in various
applications, especially for modelling heavy-tailed data. Although the
$\alpha$-stable distributions have been used in practice for many years, new
methods for identification, testing, and estimation are still being refined and
new approaches are being proposed. The constant development of new statistical
methods is related to the low efficiency of existing algorithms, especially
when the underlying sample is small or the underlying distribution is close to
Gaussian. In this paper we propose a new estimation algorithm for stability
index, for samples from the symmetric $\alpha$-stable distribution. The
proposed approach is based on quantile conditional variance ratio. We study the
statistical properties of the proposed estimation procedure and show
empirically that our methodology often outperforms other commonly used
estimation algorithms. Moreover, we show that our statistic extracts unique
sample characteristics that can be combined with other methods to refine
existing methodologies via ensamble methods. Although our focus is set on the
symmetric $\alpha$-stable case, we demonstrate that the considered statistic is
insensitive to the skewness parameter change, so that our method could be also
used in a more generic framework. For completeness, we also show how to apply
our method on real data linked to plasma physics.
