A maximum entropy distribution has been formulated in which the imposed constraint contains a stochastic (rather than a deterministic) variable. The distribution depends on the observational bin size through the smoothing of population by intrabin averaging. Moments of fluctuations calculated with this distribution give bin-size dependences (intermittency exponents) that agree reasonably with those obtained from the size dependence in nuclear multifragmentation. The exponents depend on the spread of the stochastic mechanism (supposed to be a cascading, multiplicative process) and on the magnitude of the constraint imposed. An information-theoretic interpretation is provided for the relation between statistical and mechanism-induced (dynamic) fluctuations.