  The statistics of the output activity of a neuron during its stimulation by
the stream of input impulses that forms the stochastic Poisson process is
studied. The leaky integrate-and-fire neuron is considered as a neuron model. A
new representation of the probability distribution function of the output
interspike interval durations is found. Based on it, the moment-generating
function of the probability distribution is calculated explicitly. The latter,
according to Curtiss theorem, completely determines the distribution itself. In
particular, explicit expressions are derived from the moment-generating
function for the moments of all orders. The first moment coincides with the one
found earlier. Formulas for the second and third moments have been checked
numerically by direct modeling of the stochastic dynamics of a neuron with
specific physical parameters.
