  The L\'evy distribution, alongside the Normal and Cauchy distributions, is
one of the only three stable distributions whose density can be obtained in a
closed form. However, there are only a few specific goodness-of-fit tests for
the L\'evy distribution. In this paper, two novel classes of goodness-of-fit
tests for the L\'evy distribution are proposed. Both tests are based on
V-empirical Laplace transforms. New tests are scale free under the null
hypothesis, which makes them suitable for testing the composite hypothesis. The
finite sample and limiting properties of test statistics are obtained. In
addition, a generalization of the recent Bhati-Kattumannil goodness-of-fit test
to the L\'evy distribution is considered. For assessing the quality of novel
and competitor tests, the local Bahadur efficiencies are computed, and a wide
power study is conducted. Both criteria clearly demonstrate the quality of the
new tests. The applicability of the novel tests is demonstrated with two
real-data examples.
