  Our purpose is to model the dependence between two random variables, taking
into account a priori knowledge on these variables. For example, in many
applications (oceanography, finance...), there exists an order relation between
the two variables; when one takes high values, the other cannot take low
values, but the contrary is possible. The dependence for the high values of the
two variables is, therefore, not symmetric.
  However a minimal dependence also exists: low values of one variable are
associated with low values of the other variable. The dependence can also be
extreme for the maxima or the minima of the two variables. In this paper, we
construct step by step asymmetric copulas with asymptotic minimal dependence,
and with or without asymptotic maximal dependence, using mixture variables to
get at first asymmetric dependence and then minimal dependence. We fit these
models to a real dataset of sea states and compare them using Likelihood Ratio
Tests when they are nested, and BIC- criterion (Bayesian Information criterion)
otherwise.
