  We perform statistical analysis on discrete nonlinear waves generated though
modulational instability in the context of the Salerno model that interpolates
between the intergable Ablowitz-Ladik (AL) equation and the nonintegrable
discrete nonlinear Schrodinger (DNLS) equation. We focus on extreme events in
the form of discrete rogue or freak waves that may arise as a result of rapid
coalescence of discrete breathers or other nonlinear interaction processes. We
find power law dependence in the wave amplitude distribution accompanied by an
enhanced probability for freak events close to the integrable limit of the
equation. A characteristic peak in the extreme event probability appears that
is attributed to the onset of interaction of the discrete solitons of the AL
equation and the accompanied transition from the local to the global
stochasticity monitored through the positive Lyapunov exponent of a nonlinear
map.
