  The modulational instability in the class of NLS equations is discussed using
a statistical approach. A kinetic equation for the two-point correlation
function is studied in a linear approximation, and an integral stability
equation is found. The modulational instability is associated with a positive
imaginary part of the frequency. The integral equation is solved for different
types of initial distributions (delta-function, Lorentzian) and the results are
compared with those obtained using a deterministic approach. The differences
between modulation instability of the normal NLS equation and derivative NLS
equations is emphasized.
