  We consider the family of one-dimensional maps arising from the contracting
Lorenz attractors studied by Rovella. Benedicks-Carleson techniques were used
by Rovella to prove that there is a one-parameter family of maps whose
derivatives along their critical orbits increase exponentially fast and the
critical orbits have slow recurrent to the critical point. Metzger proved that
these maps have a unique absolutely continuous ergodic invariant probability
measure (SRB measure).
  Here we use the technique developed by Freitas and show that the tail set
(the set of points which at a given time have not achieved either the
exponential growth of derivative or the slow recurrence) decays exponentially
fast as time passes. As a consequence, we obtain the continuous variation of
the densities of the SRB measures and associated metric entropies with the
parameter. Our main result also implies some statistical properties for these
maps.
