  We study the Jeffreys prior of the skewness parameter of a general class of
scalar skew--symmetric models. It is shown that this prior is symmetric about
0, proper, and with tails $O(\lambda^{-3/2})$ under mild regularity conditions.
We also calculate the independence Jeffreys prior for the case with unknown
location and scale parameters. Sufficient conditions for the existence of the
corresponding posterior distribution are investigated for the case when the
sampling model belongs to the family of skew--symmetric scale mixtures of
normal distributions. The usefulness of these results is illustrated using the
skew--logistic model and two applications with real data.
