  The term \emph{moderate deviations} is often used in the literature to mean a
class of large deviation principles that, in some sense, fill the gap between a
convergence in probability to zero (governed by a large deviation principle)
and a weak convergence to a centered Normal distribution. In this paper we
present some examples of classes of large deviation principles of this kind,
but the involved random variables converge weakly to Gumbel, exponential and
Laplace distributions.
