  We consider a type of intermittent behavior that occurs as the result of the
interplay between dynamical mechanisms giving rise to type-II intermittency and
random dynamics. We analytically deduce the law for the distribution of the
laminar phases, which has never been obtained hitherto. The already known
dependence of the mean length of the laminar phases on the criticality
parameter [PRE 68 (2003) 036203] follows as a corollary of the carried out
research. We also prove that this dependence obtained earlier under the
assumption of the fixed form of the reinjection probability does not depend on
the relaminarization properties, and, correspondingly, the obtained expression
of the mean length of the laminar phases on the criticality parameter remains
correct for different types of the reinjection probability.
