  The selection of a specific statistical distribution is seldom a simple
problem. One strategy consists in testing different distributions (normal,
lognormal, Weibull, etc.), and selecting the one providing the best fit to the
observed data and being the most parsimonious. Alternatively, one can make a
choice based on theoretical arguments and simply fit the corresponding
parameters to the observed data. In either case, different distributions can
give similar results and provide almost equivalent results. Model selection can
be more complicated when the goal is to describe a trend in the distribution of
a given variable. In those cases, changes in shape and skewness are difficult
to represent by a single distributional form. As an alternative to the use of
complicated families of distributions as models for data, the S-distribution
[{\sc Voit, E.O. }(1992) Biom.J. 7:855-878] provides a highly flexible
mathematical form in which the density is defined as a function of the
cumulative. Besides representing well-known distributions, S-distributions
provide an infinity of new possibilities that do not correspond with known
classical distributions. In this paper we obtain an analytical solution for the
quantile equation that highly simplifies the use of S-distributions. We show
the utility of this solution in different applications. After classifying the
different qualitative behaviors of the S-distribution in parameter space, we
show how to obtain different S-distributions that accomplish specific
constraints. One interesting case is the possibility of obtaining distributions
that acomplish P(X <= X_c)=0. Then, we show that the quantile solution
facilitates the use of S-distributions in Monte-Carlo experiments through the
generation of random samples. Finally, we show how to fit an S-distribution to
actual data, so that the resulting distribution can be used as a statistical
model for them.
