A mathematical model is derived for the probability distribution of neutron signal multiples inside randomly and signal triggered time intervals for a generalized time response function of the neutron detector assembly. The theory is applied to assemblies with an exponential time decay of its neutron population. The probability distributions, their factorial moments, and moments are expressed as a function of the spontaneous fission rate, (α-n) reaction rate, neutron detection probability, probability that a neutron generates a fast fission, and nuclear data. Measurements with a plutonium sample are analyzed to check the derived algorithms for the factorial moments of the two probability distributions.